International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 70, Pages 3877-3884
doi:10.1155/S0161171204401409

Bounds for total antieigenvalue of a normal operator

Sk. M. Hossein,1 K. C. Das,2 L. Debnath,3 and K. Paul4

 1Department of Mathematics, Jhargram Raj College, Vidyasagar University, Jhargram Midnapore 721507, West Bengal, India
2Department of Mathematics, Jadavpur University, Calcutta 700032, West Bengal, India
3Department of Mathematics, The University of Texas – Pan American, 1201 West University Drive, Edinburg 78539, TX, USA
4Department of Mathematics, New Alipore College, University of Calcutta, New Alipore, Calcutta 700053, West Bengal, India
Received 12 January 2004; Revised 22 March 2004

Abstract

We give an alternative proof of a theorem of Gustafson and Seddighin (1993) following the idea used by Das et al. in an earlier study of antieigenvectors (1998). The result proved here holds for certain classes of normal operators even if the space is infinite dimensional.