IJPAM: Volume 76, No. 5 (2012)

ON THE PROPERTY (BAW)

Anuradha Gupta$^1$, Neeru Kashyap$^2$
$^1$Department of Mathematics
Delhi College of Arts and Commerce
University of Delhi
Netaji Nagar, New Delhi, 110023, INDIA
$^2$Department of Mathematics
Bhaskaracharya College of Applied Sciences
University of Delhi
Dwarka, New Delhi, 110075, INDIA


Abstract. In this paper we introduce and study the property (Baw). We show that if $T$ is a bounded linear operator acting on a Banach space $X$, then property (Baw) holds for $T$ if and only if generalized a-Browder's theorem holds for $T$ and $\pi ^a(T)=E_0^a (T)$, where $\pi^a(T)$ is the set of left poles of $T$ and $E_0^a (T)$ is the set of eigen values of finite multiplicity which are isolated in the approximate spectrum. We explore conditions on Hilbert space operators $T$ and $S$ so that property (Baw) holds for $T\oplus S$.

Received: June 8, 2011

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

Key Words and Phrases: Weyl's theorem, generalized a-Weyl's theorem, generalized a-Browder's theorem, property (Baw)

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 5