IJPAM: Volume 106, No. 2 (2016)

ON LOCAL SPECTRAL PROPERTIES
OF $\lambda$-COMMUTING OPERATORS

Abdelaziz Tajmouati$^1$, Abdeslam El Bakkali$^2$, M.B. Mohamed Ahmed$^3$
$^{1,3}$Sidi Mohamed Ben Abdellah University
Faculty of Sciences Dhar El Marhaz
Fez, MOROCCO
$^{2}$Chouaib Dokkali University
Faculty of Sciences
El Jadida, MOROCCO


Abstract. Let $\mathcal{B}(X)$ be the Banach algebra of all bounded operators on a complex Banach space $X$, for a scalar $\lambda\in\mathbb{C}$ two operators $T, S\in \mathcal{B}(X)$ are said to $\lambda$-commute if $TS =\lambda ST$. If it holds, we show that $TS$ and $ST$ have many basic local spectral properties in common.

Received: September 11, 2015

AMS Subject Classification:

Key Words and Phrases: spectrum, operator equation, $\lambda$-commutativity, local spectral properties

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DOI: 10.12732/ijpam.v106i2.7 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: 106
Issue: 2
Pages: 429 - 442


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