Abstract and Applied Analysis
Volume 2012 (2012), Article ID 204031, 11 pages
http://dx.doi.org/10.1155/2012/204031
Research Article

More on ( 𝜶 , 𝜷 ) -Normal Operators in Hilbert Spaces

Rasoul Eskandari, Farzollah Mirzapour, and Ali Morassaei

Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan 45195-313, Iran

Received 18 November 2011; Revised 3 July 2012; Accepted 20 July 2012

Academic Editor: Gerd Teschke

Copyright © 2012 Rasoul Eskandari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study some properties of ( 𝛼 , 𝛽 ) -normal operators and we present various inequalities between the operator norm and the numerical radius of ( 𝛼 , 𝛽 ) -normal operators on Banach algebra ℬ( ℋ ) of all bounded linear operators 𝑇 ∶ ℋ → ℋ , where ℋ is Hilbert space.