Displaying similar documents to “The Kato-type spectrum and local spectral theory”

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.

A note on preservation of spectra for two given operators

Carlos Carpintero, Alexander Gutiérrez, Ennis Rosas, José Sanabria (2020)

Mathematica Bohemica

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We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators...

On totally * -paranormal operators

Eungil Ko, Hae-Won Nam, Young Oh Yang (2006)

Czechoslovak Mathematical Journal

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In this paper we study some properties of a totally * -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally * -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally * -paranormal operators through the local spectral theory. Finally, we show that every totally * -paranormal operator satisfies an analogue of the single valued extension property for W 2 ( D , H ) and some of totally * -paranormal operators have scalar...

Restriction of an operator to the range of its powers

M. Berkani (2000)

Studia Mathematica

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Let T be a bounded linear operator acting on a Banach space X. For each integer n, define T n to be the restriction of T to R ( T n ) viewed as a map from R ( T n ) into R ( T n ) . In [1] and [2] we have characterized operators T such that for a given integer n, the operator T n is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where T n belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with...