A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity

• Autorzy: Vasile Lauric
• Języki publikacji: EN

Abstrakty

EN

We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.

Słowa kluczowe

EN

Hilbert-Schmidt and trace-class operators; Almost normal operators; Almost hyponormal operators; Modulus of quasi-triangularity

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 8-14

Daty

otrzymano

2015-06-07

zaakceptowano

2016-01-09

online

2016-03-10

Twórcy

autor

Vasile Lauric

• Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, USA

Bibliografia

• [1] A. Abdessemed and E. B. Davies, Some commutator estimates in the Schatten classes, J. London Math. Soc. (2), 41, 1989, 299-308
• [2] T. Furuta, An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality, Proc. Amer. Math. Soc., 81, 1981, 240–242
• [3] D. Hadwin and E. Nordgren, Extensions of the Berger-Shaw theorem, Proc. Amer. Math. Soc., 102, 1988, 517–525
• [4] E. Kissin, D. Potapov, V. Shulman and F. Sukochev, Operator smoothness in Schatten norms for functions of several variables: Lipschitz conditions, differentiability and unbounded derivations, Proc. London Math. Soc. (4), 105, 2012, 661–702
• [5] F. Kittaneh, On generalized Fuglede-Putnam theorems of Hilbert-Schmidt type, Proc. Amer. Math. Soc., 88, 1983, 293–298
• [6] F. Kittaneh, On Lipschitz functions of normal operators, Proc. Amer. Math. Soc., 94, 1985, 416–418
• [7] T. Nakazi, Complete spectral area estimates and self-commutators, Michigan Math. J., 35, 1988, 435–441
• [8] V. Shulman, Some remarks on the Fuglede-Weiss theorem, Bull. London Math. Soc. (4), 28, 1996, 385-392
• [9] V. Shulman and L. Turowska, Operator Synthesis II. Individual synthesis and linear operator equations, J. für die reine und angewandte Math. (590), 2006, 2006, 143–187
• [10] D. Voiculescu, Some extensions of quasitriangularity, Rev. Roumaine Math. Pures Appl., 18, 1973, 1303–1320
• [11] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators, J. Operator Theory, 2, 1979, 3–37
• [12] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators II, J. Operator Theory, 5, 1981, 77–100
• [13] D. Voiculescu, A note on quasitriangularity and trace-class self-commutators, Acta Sci. Math. (Szeged), 42, 1980, 195–199
• [14] D. Voiculescu, Remarks on Hilbert-Schmidt perturbations of almost normal operators, Topics in Modern Operator Theory; Operator Theory: Advances and Applications-Birkhäuser, 2, 1981, 311–318
• [15] D. Voiculescu, Almost Normal Operators mod Hilbert-Schmidt and the K-theory of the Algebras EΛ(Ω), arXiv:1112.4930v2
• [16] D. Voiculescu, Hilbert space operators modulo normed ideals, Proc. Int. Congress Math., 1983, 1041–1047
• [17] G. Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. math. Soc., 83, 1981, 113–118
• [18] G. Weiss, Fuglede’s commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators. II, J. Operator Theory, 5, 1981, 3–16

Identyfikatory

DOI

10.1515/conop-2016-0002