Books:

1. D. Petz, An invitation to the algebra of the canonical commutation relation:
   Leuven University Press, Leuven, 1990.
2. M. Ohya and D. Petz, Quantum Entropy and Its Use:
   Springer-Verlag, Heidelberg, 1993. Secon edition 2004.
3. F. Hiai and D. Petz, The semicircle law, free random variables and entropy:
   American Mathematical Society, Providence, 2000
4. Petz Dénes, Lineáris Analízis (in Hungarian):
   Akadémiai Kiadó, Budapest, 2002.

Research Papers:

1. D. Petz, A characterization of the class of compact spaces: Studia Sci. Math. Hungar. 12(1977), 407-408.
2. D. Petz, Compactness as E-pseudocompactness: Commentationes Math. Univ. Carolinae 19(1978), 309-314.
3. D. Petz, On a problem of D. Newman: Acta Math. Acad. Sci. Hungar. 32(1978), 161-162.
4. D. Petz, Direct integral of multifunctions into von Neumann algebras:
   Studia Sci. Math. Hungar. 18(1978), 239-245.
5. D. Petz, On (E,k)-compact spaces:
   Colloq. Math. Soc. J. Bólyai 23(1980), 945-955.
6. D. Petz, Genaralized connectedness and disconnectedness in topology:
   Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 24(1980), 247-252.
7. D. Petz, On box product of syntopogenous spaces:
   Acta Math. Acad. Sci. Hungar. 36(1980), 91-97.
8. D. Petz, On the class of compact topological spaces:
   Mat. Lapok, 28(1980), 91-97. (in Hungarian)
9. D. Petz, On center-valued states of von Neumann algebras:
   Acta Sci. Math. 43(1981), 219-228.
10. D. Petz, A characterization of the canonical centre-valued trace in finite von Neumann algebras:
    J. London Math. Soc. 23(1981), 329-331.
11. D. Petz, Locally compact topological groups: Group von Neumann algebra and duality
    Mat. Lapok, 29(1981), 329-341. (in Hungarian)
12. D. Petz, On spectral and central states of Banach algebras:
    Acta Math. Hungar. 42(1983), 19-24.
13. D. Petz, Direct integral of multifunctions into von Neumann algebras:
    Studia Sci. Math. Hungar. 18(1983), 239-245.
14. D. Petz, On the finiteness of operator algebras with respect to an automorphism group:
    Rend. Math. 7(1983), 483-489.
15. D. Petz, Fixed points and mean ergodic theorems:
    Colloq. Math. Soc. J. Bólyai, 35(1983), 949-956.
16. D. Petz, Ergodic theorems in von Neumann algebras:
    Acta Sci. Math. 46(1984), 329-344.
17. D. Petz, Quasi-uniform ergodic theorems in von Neumann algebras:
    Bull. London Math. Soc. 16(1984), 151-156.
18. D. Petz, Ergodic theorems in von Neumann algebras:
    Functional Analysis: Surveys and Recent Results III, 189-196, Nort-Holland (1984).
19. D. Petz, Quantum ergodic theorems:
    Quantum Probability and Applications to the Quantum Theory of Irreversible Processes, Lecture Notes in Math. No. 1055(1984), 289-300, Springer.
20. D. Petz, A dual in von Neumann algebras with weights:
    Quart. J. Math. Oxford, 35(1984), 475-483.
21. D. Petz, A mean ergodic theorem with a look at martingales:
    Studia Sci. Math. Hungar. 19(1984), 77-80.
22. D. Petz, The relative entropy of states of a von Neumann algebra:
    Proc. Second Int. Conf. on Operator Algebras, Ideals and their Appl. in Theoretical Phys., Teubner Texte zur Math. No.67(1984), 112-117.
23. D. Petz, Spectral scale of selfadjoint operators and trace inequalities:
    J. Math. Anal. Appl. 109(1985), 74-82.
24. C. Cecchini, D. Petz, Norm convergence of generalized martingales in L^p-spaces over von Neumann algebras:
    Acta Sci. Math. 48(1985), 55-63.
25. D. Petz, Properties of quantum entropy:
    Quantum Probability and Applications, Lecture Notes in Math. No.1136(1985), 428-441, Springer.
26. D. Petz, Quasi-entropies for states of a von Neumann algebra:
    Publ. RIMS. Kyoto Univ. 21(1985), 781-800.
27. D. Petz, On invariant conditional expectations in von Neumann algebras:
    Annales Univ. Sci. 29(1986), 227-229.
28. D. Petz, The equality of generalized conditional expectations on von Neumann algebras:
    Semesterbericht Funktionalanalysis 85/86(1986), 117-125, Tübingen Uni.
29. D. Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra:
    Commun. Math. Phys. 105(1986), 123-131.
30. D. Petz, Almost uniform convergence on the predual of a von Neumann algebra and an ergodic theorem:
    Aspects of Positivity in Functional Analysis, 247-254, Elsevier (1986).
31. D. Petz, Properties of the relative entropy of states of von Neumann algebras:
    Acta Math. Hungar., 47(1986), 65-72.
32. D. Petz, Quasi-entropies for finite quantum systems:
    Rep. Math. Phys., 23(1986), 57-65.
33. D. Petz, On the equality in Jensen's inequality for operator convex functions:
    Integral Equations Op. Theory, 5(1986), 744-747.
34. D. Petz, Jensen's inequality for contractions on operator algebras:
    Proc. Amer. Math. Soc., 99(1987), 273-277.
35. D. Petz, A variational expression for the relative entropy:
    Commun. Math. Phys., 114(1988), 345-348.
36. D. Petz, Sufficiency of channels over von Neumann algebras:
    Quart. J. Math. Oxford, 39(1988), 907-1008.
37. D. Petz, Conditional expectation in quantum probability:
    Quantum Probability and Applications, Lecture Notes in Math., 1303(1988), 251-260.
38. D. Petz, J. Zemánek, Characterizations of the trace:
    Linear Algebra and Appl., 111(1988), 43-52.
39. D. Petz, Irreducible mappings of finite dimensional C*-algebras:
    Semesterbericht Functionalanalysis, 14(1988), 163-168.
40. C. Cecchini, D. Petz, On the Fixed Point Algebras for j-conditional expectations in von Neumann Algebras:
    Studia Sci. Math. Hungar., 24(1989), 133-137.
41. D. Petz, Characterization of sufficient observation channels:
    Mathematical Methods in Statistical Mechanics, 167-178, Leuven University Press (1989).
42. D. Petz, G. A. Raggio and A. Verbeure, Asymptotics of Varadhan-type and the Gibbs variational principle:
    Commun. Math. Phys., 121(1989), 271-282.
43. D. Petz, Positive mappings of matrix algebras:
    Quantum Probability and Applications IV, Lecture Notes in Math., 1396(1989), 295-303.
44. C. Cecchini, D. Petz, State extensions and a Radon-Nikodym theorem for conditional expectations on von Neumann algebras:
    Pacific J. Math., 138(1989), 9-24.
45. D. Petz, A de Finetti-type theorem with m-dependent states:
    Prob. Th. Rel. Fields, 85(1990), 1-11.
46. C. Cecchini, D. Petz, Classes of conditional expectations over von Neumann algebras:
    J. Functional Anal., 92(1990), 8-29.
47. D. Petz, First steps towards a Donsker and Varadhan theory in operator algebras:
    Quantum Probability and Applications IV, Lecture Notes in Math., 1442(1990), 311-319.
48. D. Petz, On certain property of the relative entropy of states of operator algebras:
    Math. Zeitschrift 206(1991), 351-361.
49. C. Cecchini, D. Petz, A stochastic transition for von Neumann algebras:
    Bolletino U.M.I. (7)5-A(1991), 181-186.
50. F. Hiai, D. Petz, The proper formula for relative entropy and its asymptotics in quantum probability:
    Commun. Math. Phys. 143(1991), 99-114.
51. D. Petz, Entropy, the central limit theorem and the algebra of the canonical commutation relation:
    Lett. Math. Phys. 24(1992), 211-220.
52. D. Petz, Characterization of the relative entropy of states of matrix algebras:
    Acta Math. Hungar. 59(1992), 449-455.
53. H. Muraki, M. Ohya, D. Petz, Entropies of general quantum states:
    Open Syst. Inf. Dynamics 1(1992), 43-56.
54. D. Petz, Entropy in quantum probability I:
    in Quantum Probability and Related Topics VII, 275-297 (World Scientific, Singapore, 1992)
55. F. Hiai, D. Petz, The Golden-Thompson trace inequality is complemented:
    Linear Alg. Appl. 181(1993), 153-185.
56. D. Petz, An application of a lemma of Riesz and Sz.-Nagy:
    Acta Sci. Math. 57(1993), 221-228
57. C. Cecchini, D. Petz, Chain rules for canonical state extensions on von Neumann algebras:
    Colloq. Math. 64(1993), 115-119.
58. D. Petz, G. Toth, The Bogoliubov inner product in quantum statistics:
    Lett. Math. Phys. 27(1993), 205-216.
59. D. Petz, On entropy functionals of states of operator algebras:
    Acta Math. Hungar. 64(1994), 279-286.
60. F. Hiai, D. Petz, Entropy densities for Gibbs states of quantum spin systems:
    Rev. Math. Phys. 5, 693-712 (1994)
61. D. Petz, Geometry of canonical correlation on the state space of a quantum system:
    J. Math. Phys. 35(1994), 780-795
62. D. Petz, Discrimination between states of a quantum system by observations:
    J. Functional Anal. 120(1994), 82-97
63. D. Petz, Entropy of Markov states:
    Riv. di Math. Pura ed Appl. 14(1994), pp. 33-42
64. D. Petz, A survey of trace inequalities:
    in Functional Analysis and Operator Theory, 287-298, Banach Center Publications, 30 (Warszawa 1994)
65. F. Hiai, D. Petz, Entropy density for algebraic states:
    J. Functional Anal. 125(1994), 287-308
66. F. Hiai, M. Ohya, D. Petz, McMillan type convergence for quantum Gibbs states:
    Arch. der Math. 65(1995), 154-158
67. M. Ohya, D. Petz, Notes on quantum entropy:
    Studia Sci. Math. Hungar. 31(1996), 423-430
68. D. Petz, Monotone metrics on matrix spaces:
    Linear Algebra Appl. 244(1996), 81-96
69. F. Hiai, D. Petz, G.Toth, Curvature in the geometry of canonical correlation:
    Studia Sci. Math. Hungar. 32(1996), 235-249
70. D. Petz, Cs. Sudár, Geometries of quantum states:
    J. Math. Phys. 37(1996), 2662-2673
71. D. Petz, H. Hasegawa, On the Riemannian metric of a-entropies of density matrices:
    Lett. Math. Phys. 38(1996), 221-225
72. D. Petz, Entropy density in quantum statistical mechanics and information theory:
    in Contributions in Probability, ed. C. Cecchini, 221-226, Forum, Udine, 1996,
73. F. Hiai, D. Petz, Quantum mechanics in AF C*-systems:
    Rev. Math. Phys. 8(1996), 819-859
74. F. Oravecz, D. Petz, On the eigenvalue distribution of some symmetric random matrices:
    Acta Sci. Math. 63(1997), 483-495
75. H. Hasegawa, D. Petz, Non-commutative extension of information geometry II:
    in Quantum Communication, Computing, and Measurement, ed. O. Hirota et al, Plenum, 1997
76. M. Ohya, D. Petz, N. Watanabe, On capacities of quantum channels:
    Prob. Math. Stat. 17(1997), 179-196
77. D. Petz, M.B. Ruskai, Contraction of generalized relative entropy under stochastic mappings on matrices:
    Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1(1998), 83-90
78. D. Petz, F. Hiai, Logarithmic energy as entropy functional:
    in Advances in Differential Equations and Mathematical Physics (eds: E. Carlen, E.M. Harrell, M. Loss), Contemporary Math. 217(1998), 205-221
79. F. Hiai, D. Petz, Maximizing free entropy:
    Acta Math. Hungar., 80(1998), 325-346
80. D. Petz, Information geometry of quantum states:
    in Quantum Probability Communications, vol. 10, ed. R.L. Hudson et al, World Scientific, 135-158, 1998
81. F. Hiai, D. Petz, Eigenvalue density of the Wishart matrix and large deviations:
    Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1(1998), 633-646.
82. M. Ohya, D. Petz, N. Watanabe, Numerical computation of quantum capacity:
    Int. J. Theor. Phys. 37(1998), 507-510
83. F. Hiai, D. Petz, Properties of free entropy related to polar decomposition:
    Commun. Math. Phys. 202(1999), 421-444
84. D. Petz, Cs. Sudár, Extending the Fisher metric to density matrices:
    in Geometry in Present Days Science, eds. O.E. Barndorff-Nielsen and E.B. Vendel Jensen, 21-34, 1999.
85. D. Petz, Relative entropy in quantum information theory:
    in mini-proceedings of the conference Stochastics and Quantum Physics, MaPhySto, University of Aarhus, Miscellanea, No. 16, 1999
86. D. Petz, A. Jencová, On quantum Fisher information:
    J. Electrical Engineering, 78-81, 50, 1999
87. F. Hiai, D. Petz, A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices:
    Ann. Inst. Henri Poincaré, Probabilités et Statistiques 36(2000), 71-85
88. P.W. Michor, D. Petz and A. Andai, On the curvature of a certain Riemannian space of matrices:
    Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3(2000), 199-212
89. F. Hiai and D. Petz, Asymptotic freeness almost everywhere for random matrices:
    Acta Sci. Math (Szeged), 66(2000), 801-826
90. D. Petz and M. Mosonyi, Stationary quantum source coding:
    J. Math. Phys. 42(2001), 4857-4864.
91. F. Hiai, M. Mizuo and D. Petz, Free relative entropy for measures and a corresponding perturbation theory:
    J. Math. Soc. Japan, 54(2002), 679-718.
92. M. Fannes and D. Petz, On the function Tr exp(A+itB):
    Int. J. Math. and Math. Sci. 29(2002), 389-394.
93. D. Petz, Covariance and Fisher information in quantum mechanics:
    J. Phys. A: Math. Gen. 35(2002), 929-939
94. D. Petz, Monotonicity of quantum relative entropy revisited:
    Rev. Math. Phys. 15(2003), 79-91.
95. M. Fannes and D. Petz, Perturbation of Wigner matrices and a conjecture:
    Proc. Amer. Math. Soc. 131(2003), 1981-1988.
96. P. Hayden, R. Jozsa, D. Petz and A. Winter, Structure of states which satisfy strong subadditivity of quantum entropy with equality:
    Commun. Math. Phys. 246(2004), 359-374
97. D. Petz and J. Réffy, On asymptotics of large Haar distributed unitary matrices:
    Period. Math. Hungar. 49(2004), 103-117.
98. D. Petz and J. Réffy, Large deviation theorem for empirical eigenvalue density of truncated Haar unitary matrices:
    to be published in Prob. Theory Rel. Fields.
99. M. Mosonyi and D. Petz, Structure of sufficient quantum coarse-grainings:
    Lett. Math. Phys. 68(2004), 19-30.
100. F. Hiai, D. Petz and Y. Ueda, Free transportation cost inequalities via random matrix approximation:
     Prob. Theory Rel. Fields. 130(2004), 199-221.
101. D. Petz, Quantum source coding and data compression:
     to be published in the proceedings of Conference on Search and Communication Complexity, Bolyai Studies.
102. F. Hiai, D. Petz and Y. Ueda, A free logarithmic Sobolev inequality on the circle:
     to be published in Canadian Math. Bulletin
103. M. A. Nielsen and D. Petz, A simple proof of the strong subadditivity inequality:
     Quantum Information & Computation, 5(2005), 507-513.
104. N. Akiho, F. Hiai and D. Petz, Equilibrium states and entropy densities in gauge-invariant C*-systems:
     Rev. Math. Phys. 17(2005), 365-389.
105. A. Jencova and D. Petz, Sufficiency in quantum statistical inference:
     to be published in Commun. Math. Phys.
106. D. Petz and R. Temesi, Means of positive numbers and matrices:
     to be published in SIAM Journal on Matrix Analysis and Applications.
107. F. Hiai and D. Petz, A free analogue of the transportation cost inequality on the circle (dedicated to András Prékopa on the occasion of his 70th birthday):
     to be published.
108. F. Hiai and D. Petz, Large deviations for functions of two random projections:
     to be published.
109. D. Petz, Means of positive matrices: Geometry and a conjecture:
     to be published.

Other publications

1. D. Petz, Quantum mechanics in view of information:
   Kagaku, 63, 569-574 (1993) (in Japanese).
2. D. Petz and M. Rédei, John von Neumann and the theory of operator algebras:
   in The Neumann Compendum, 163-185, eds. F. Bródi, T. Vámos, World Scientific Series in 20th Century Math. vol. 1, World Scientific, Singapore, 1995.
3. Petz D., Mérték és dimenzió:
   Természet Világa, 1997/3 (in Hungarian).
4. D. Petz and G.J. Székely, Die Entropie:
   in Jenseits von Kunst, Peter Weibel, Passagen Verlag, 1998.
5. D. Petz, Mathematical information theory:
   in Enciclopedia Italiana.
6. Petz D., A q-világa, avagy a matematika deformációja:
   Polygon, VIII(1999), 35-44 (in Hungarian).
7. D. Petz, Entropy, von Neumann and the von Neumann entropy:
   in John von Neumann and the Foundations of Quantum Physics, eds. M. Rédei and M. Stöltzner, Kluwer, 2001
8. Petz D., Neumann János tudományos öröksége:
   Természet Világa, 2004. január (in Hungarian).
9. Petz D., Neumann János tudományos öröksége:
   Debreceni Szemle, 2005. január (in Hungarian)
10. Á. Császár and D. Petz, A panorama of Hungarian real and functional analysis in the 20th century:
    to be published
11. Petz Dénes: Lax Péter Abel-díjas, Népszabadság, 2005. március 19.
12. Petz Dénes: Mátrixok, nagy eltérések és egyenlőtlenségek, to be published.
13. Kovács Veronika és Petz Dénes: Számtani közép, mértani közép, meg ilyenek, to be published.