Abstract and Applied Analysis
Volume 2012 (2012), Article ID 846396, 13 pages
http://dx.doi.org/10.1155/2012/846396
Research Article

Numerical Range of Two Operators in Semi-Inner Product Spaces

N. K. Sahu,1 C. Nahak,1 and S. Nanda2

1Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
2KIIT University, Bhubaneswar 751024, India

Received 9 January 2012; Revised 18 January 2012; Accepted 1 February 2012

Academic Editor: Michiel Bertsch

Copyright © 2012 N. K. Sahu 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

In this paper, the numerical range for two operators (both linear and nonlinear) have been studied in semi-inner product spaces. The inclusion relations between numerical range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum have been established for two linear operators. We also show the inclusion relation between approximate point spectrum and closure of the numerical range for two nonlinear operators. An approximation method for solving the operator equation involving two nonlinear operators is also established.