WEYL'S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T*k|T2|Tk≥T*k|T|2Tk

Title & Authors
WEYL'S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T*k|T2|Tk≥T*k|T|2Tk
Kim, In-Hyoun;

Abstract
For a bounded linear operator T on a separable complex infinite dimensional Hilbert space $\small{\mathcal{H}}$, we say that T is a quasi-class (A, k) operator if $\small{T^{*k}|T^2|T^k\;{\geq}\;T^{*k}|T|^2T^k}$. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl's theorem. Also, we consider the tensor product for quasi-class (A, k) operators.
Keywords
quasi-class (A, k) operator;Weyl's theorem;tensor product;
Language
English
Cited by
1.
WEYL'S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS An* OPERATO,Hoxha, Ilmi;Braha, Naim Latif;

대한수학회지, 2014. vol.51. 5, pp.1089-1104
1.
WEYL'S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS An*OPERATO, Journal of the Korean Mathematical Society, 2014, 51, 5, 1089
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