generalized weyl’s theorem
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Author(s):  
Mohammad H.M. Rashid ◽  
T. Prasad

In this paper, we study Weyl type theorems for $f(T)$, where $T$ is algebraically class $p$-$wA(s, t)$ operator with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$ and $f$ is an analytic function defined on an open neighborhood of the spectrum of $T$. Also we show that if $A , B^{*} \in B(\mathcal{H}) $ are class $p$-$wA(s, t)$ operators with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$,then generalized Weyl's theorem , a-Weyl's theorem, property $(w)$, property $(gw)$ and generalized a-Weyl's theorem holds for $f(d_{AB})$ for every $f \in H(\sigma(d_{AB})$, where $ d_{AB}$ denote the generalized derivation $\delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\delta_{AB}(X)=AX-XB$ or the elementary operator $\Delta_{AB}:B(\mathcal{H})\rightarrow B(\mathcal{H})$ defined by $\Delta_{AB}(X)=AXB-X$.



2013 ◽  
Vol 59 (1) ◽  
pp. 163-172
Author(s):  
Salah Mecheri

Abstract Let H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the algebra of all bounded linear operators on H. Let A;B be operators in B(H). In this paper we prove that if A is quasi-class A and B* is invertible quasi-class A and AX = XB, for some X ∈ C2 (the class of Hilbert-Schmidt operators on H), then A*X = XB*. We also prove that if A is a quasi-class A operator and f is an analytic function on a neighborhood of the spectrum of A, then f(A) satisfies generalized Weyl's theorem. Other related results are also given.



2012 ◽  
Vol 25 (4) ◽  
pp. 655-668 ◽  
Author(s):  
D. Senthilkumar ◽  
P. Maheswari Naik ◽  
N. Sivakumar










2011 ◽  
Vol 27 (1) ◽  
pp. 24-33
Author(s):  
C. CARPINTERO ◽  
◽  
D. MUNOZ ◽  
E. ROSAS ◽  
O. GARCIA ◽  
...  

In this paper we establish necessary and sufficient conditions on bounded linear operators for which generalized Weyl’s theorem, or generalized a-Weyl theorem, holds. We also consider generalized Weyl’s theorems in the framework of polaroid operators and obtain improvements of some results recently established in [20] and [29].



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