International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 761-766
Structure of the antieigenvectors of a strictly accretive operator
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
is an antieigenvector of a
strictly accretive operator 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
and if the first antieigenvalue, which is equal to min is attained at the unit vector .