Isolated points of spectrum of (p, k)-quasihyponormal operators
TLDR
In this article, it was shown that if λ 0 is an isolated point of σ(T), then E is self-adjoint and EH =ker(T−λ 0)∗, then EH=ker( Tk).About:
This article is published in Linear Algebra and its Applications.The article was published on 2004-05-01 and is currently open access. It has received 38 citations till now.read more
Citations
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Journal ArticleDOI
Property (w) and perturbations II
TL;DR: Aiena et al. as discussed by the authors showed that property (w ) in general is not preserved under finite-dimensional perturbations commuting with a bounded operator T acting on a Banach space, under the assumption that T is a-isoloid.
Journal ArticleDOI
On Wold-type decomposition
TL;DR: In this article, the Wold-type decomposition is applied to (p, k ) -quasihyponormal, k * -paranormal, and k -par-anormal operators.
Journal ArticleDOI
Continuity of the spectrum on a class of upper triangular operator matrices
B. P. Duggal,I. H. Jeon,I.H. Kim +2 more
TL;DR: In this paper, it was shown that the spectrum is continuous on the set C(i)⊂B(Hi) of operators A for which σ(A)={0} implies A is nilpotent (possibly, the 0 operator).
Book ChapterDOI
Quasinilpotent Part of class A or (p, k)-quasihyponormal Operators
TL;DR: In this article, the quasinilpotent part ℌ 0(T − λ) = {x ∈ ∌: \( \mathop {\lim }\limits_{n \to \infty } \left\| {(T - \lambda )^n x} \right\|^{\tfrac{1} {n}} = 0 \)} of a class A or (p, k)-quasihyponormal operator T.
Journal ArticleDOI
Riesz projections for a class of Hilbert space operators
TL;DR: In this paper, it was proved that if a T ∈ THN is such that the isolated eigenvalues of T are normal, then the Riesz projection Pλ associated with a λ ∈ ǫσ(T) is self-adjoint and P λ H = (T - λ ) - 1 ( 0 ) = ( T ∗ - ï¯ ) − 1( 0 ).
References
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Journal ArticleDOI
Onp-hyponormal operators for 0<p<1
TL;DR: In this paper, the generalized top-hyponormal distance formula Tt-λI−1−1 =Dist(λ, σ(T)]−1, λ∉σ(T), for hyponormal operators, is generalized for 0