Approximations of Antieigenvalue and Antieigenvalue-Type Quantities

Abstract EN

We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality.

In the second section, we approximate several antieigenvalue-type quantities for arbitrary accretive operators.

Each antieigenvalue-type quantity is approximated in terms of the same quantity for normal matrices.

In particular, we show that for an arbitrary accretive operator, each antieigenvalue-type quantity is the limit of the same quantity for a sequence of finite-dimensional normal matrices.