International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 761-766

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

Copyright © 1998 K. C. Das 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.


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)/(Aff) is attained at the unit vector f.