IJPAM: Volume 108, No. 3 (2016)

ON PSEUDO B-WEYL AND
PSEUDO B-FREDHOLM OPERATORS

Abdelaziz Tajmouati$^1$, Mohammed Karmouni$^2$
$^{1,2}$Laboratory of Mathematical Analysis and Applications
Faculty of Sciences Dhar Al Mahraz
Sidi Mohamed Ben Abdellah University
Fez, MOROCCO


Abstract. In this note, we show that the pseudo B-Fredholm and pseudo B-Weyl spectra, for a bounded linear operator on a Banach space, are compact in the complex plane. Afterwards, we prove that the pseudo B-Fredholm spectrum differs from the Kato spectrum on at most countable many points. Furthermore, if $T$ and $T^*$ have the SVEP at $\lambda_0$, we show that $\lambda_{0}I -T$ is a pseudo B-Weyl operator if and only if $\lambda_{0}I -T$ is a pseudo B-Fredholm operator.

Received: April 7, 2016

AMS Subject Classification: 47A53, 47A10, 47A11

Key Words and Phrases: pseudo B-Fredholm, pseudo B-Weyl, single-valued extension property, isolated point

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DOI: 10.12732/ijpam.v108i3.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 3
Pages: 513 - 522


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