Journal of Mathematics and Statistics

Weyl’s Theorem for Algebraically Class A(s, t) Operators

D. Senthilkumar and D. Kiruthika

DOI : 10.3844/jmssp.2012.150.153

Journal of Mathematics and Statistics

Volume 8, Issue 1

Pages 150-153

Abstract

In this study, we show that WeylÂ’s theorem holds for algebraically class A (s, t) operator acting on Hilbert space. We prove: (i) WeylÂ’s theorem holds for f (T) for every f belongs to holomorphic function of spectrum of T; (ii) generalized WeylÂ’s theorem holds for T; (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.

Copyright

© 2012 D. Senthilkumar and D. Kiruthika. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.