International Journal of Mathematics and Mathematical Sciences 
Volume 21 (1998), Issue 4, Pages 761-766
doi:10.1155/S0161171298001069

Structure of the antieigenvectors of a strictly accretive operator

K. C. Das, M. Das Gupta, and K. Paul

 Department of Mathematics, Jadavpur University, Calcutta 700 032, India
Received 10 June 1996; Revised 6 March 1997

Abstract

A necessary and sufficient condition that a vector f is an antieigenvector of a strictly accretive operator A is obtained. The structure of antieigenvectors of selfadjoint and certain class of normal operators is also found in terms of eigenvectors. The Kantorovich inequality for selfadjoint operators and the Davis's inequality for normal operators are then easily deduced. A sort of uniqueness is also established for the values of Re(Af,f) and ‖Af‖ if the first antieigenvalue, which is equal to min Re(Af,f)/(‖Af‖‖f‖) is attained at the unit vector f.