Displaying similar documents to “On totally * -paranormal operators”

A note on the a -Browder’s and a -Weyl’s theorems

M. Amouch, H. Zguitti (2008)

Mathematica Bohemica

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Let T be a Banach space operator. In this paper we characterize a -Browder’s theorem for T by the localized single valued extension property. Also, we characterize a -Weyl’s theorem under the condition E a ( T ) = π a ( T ) , where E a ( T ) is the set of all eigenvalues of T which are isolated in the approximate point spectrum and π a ( T ) is the set of all left poles of T . Some applications are also given.

The Kato-type spectrum and local spectral theory

T. L. Miller, V. G. Miller, Michael M. Neumann (2007)

Czechoslovak Mathematical Journal

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Let T ∈ ℒ ( X ) be a bounded operator on a complex Banach space X . If V is an open subset of the complex plane such that λ - T is of Kato-type for each λ ∈ V , then the induced mapping f ( z ) ↦ ( z - T ) f ( z ) has closed range in the Fréchet space of analytic X -valued functions on V . Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to a sharper estimate of Nagy’s spectral residuum of T . Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier...

Hereditarily normaloid operators.

Bhagwati Prashad Duggal (2005)

Extracta Mathematicae

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A Banach space operator T belonging to B(X) is said to be hereditarily normaloid, T ∈ HN, if every part of T is normaloid; T ∈ HN is totally hereditarily normaloid, T ∈ THN, if every invertible part of T is also normaloid; and T ∈ CHN if either T ∈ THN or T - λI is in HN for every complex number λ. Class CHN is large; it contains a number of the commonly considered classes of operators. We study operators T ∈ CHN, and prove that the Riesz projection associated with a λ ∈ isoσ(T), T ∈...