A Fuglede-Putnam type theorem for a class of almost normal operators

• Autorzy: Lauric, Vasile
• Języki publikacji: EN

Abstrakty

EN

In this note we will prove that operators T ∈ L(H) with finite k₁ function satisfy a Fuglede-Putnam type modulo the Hilbert-Schmidt class, that is, for arbitrary X ∈ L(H) with TX - XT ∈ C₂(H) implies T*X - XT* e C₂(H).

Słowa kluczowe

EN

almost normal operators; k1-function; Fuglede-Putnam type theorem

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2019
• Tom: nr 62
• Strony: 81--84
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Lauric, Vasile

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

Bibliografia

• [1] Lauric V., A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity, Concr. Oper., 3(2016), 8-14.
• [2] Voiculescu D.Y., Some results on norm-ideal perturbations of Hilbert space operators II, J. Operator Theory, 5(1981), 77-100.
• [3] Voiculescu D.Y., Hilbert space operators modulo normed ideals, Proceedings of the International Congress of Mathematicians, August 16-24, W-wa (1983), 1041-1047.
• [4] Voiculescu D.Y., Almost normal operators mod Hilbert-Schmidt and the K-theory of the algebras EA(Ω), J. Noncommut. Geom., 8(2014), 11231-1145.
• [5] Weiss G., The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. Math. Soc., 83(1981), 113-118.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).