Approximations of Antieigenvalue and Antieigenvalue-Type Quantities

Morteza Seddighin

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-15

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:318214

DOI: 10.1155/2012/318214

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