Generalised Weyl and Weyl type theorems for algebraically k-paranormal operators

If λ is a nonzero isolated point of the spectrum of k*-paranormal operator T for a positive integer k, then the Riesz idempotent operator E of T with respect to λ satisfies E^sub λ^H = ker(T - λ) = ker(T - λ)* and E^sub λ^ is self-adjoint. We prove that if T is an algebraically k*-paranormal operato...

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Bibliographic Details
Published in:Scientia magna 2012-01, Vol.8 (1), p.111-111
Main Authors: Panayappan, S, Sumathi, D, Jayanthi, N
Format: Article
Language:English
Subjects:
Algebra
Approximation
Integers
Mapping
Operators
Spectra
Theorems
Online Access:Get full text
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Summary:If λ is a nonzero isolated point of the spectrum of k*-paranormal operator T for a positive integer k, then the Riesz idempotent operator E of T with respect to λ satisfies E^sub λ^H = ker(T - λ) = ker(T - λ)* and E^sub λ^ is self-adjoint. We prove that if T is an algebraically k*-paranormal operator for a positive integer k, then spectral mapping theorem and spectral mapping theorem for essential approximate point spectrum hold for T, Generalised Weyl's theorem holds for T and other Weyl type theorems are discussed. [PUBLICATION ABSTRACT]
ISSN:1556-6706