IJPAM: Volume 34, No. 2 (2007)

OPERATORS SATISFYING $\Re \sigma_\alpha(T)=\sigma_\alpha(\Re T)$

S.C. Arora$^1$, Preeti Dharmarha$^2$
$^1$Department of Mathematics
University of Delhi
Delhi, 110 007, INDIA
e-mail: [email protected]
$^2$Department of Mathematics
Hans Raj College
University of Delhi
Delhi, 110 007, INDIA
e-mails: [email protected], [email protected]

Abstract.The notion of weighing spectra is used to show that if $T$ is a hyponormal operator, then $\Re \sigma_\alpha(T)=\sigma_\alpha(\Re T)$. The concept of approximate proper vectors is extended to prove the result for weighing spectra.

Received: October 27, 2006

AMS Subject Classification: 47A53

Key Words and Phrases: weighted spectrum, weighted approximate spectrum, $\alpha$-closed set

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 2