Approximations of Antieigenvalue and Antieigenvalue-Type Quantities

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...

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Main Author: Morteza Seddighin
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/318214
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author Morteza Seddighin
author_facet Morteza Seddighin
author_sort Morteza Seddighin
collection DOAJ
description 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.
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spelling doaj-art-1e4acf6ea1a147f8b7202dccf0c6b2c22025-08-20T02:04:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/318214318214Approximations of Antieigenvalue and Antieigenvalue-Type QuantitiesMorteza Seddighin0Mathematics Department, Indiana University East, Richmond, IN 47374, USAWe 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.http://dx.doi.org/10.1155/2012/318214
spellingShingle Morteza Seddighin
Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
International Journal of Mathematics and Mathematical Sciences
title Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
title_full Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
title_fullStr Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
title_full_unstemmed Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
title_short Approximations of Antieigenvalue and Antieigenvalue-Type Quantities
title_sort approximations of antieigenvalue and antieigenvalue type quantities
url http://dx.doi.org/10.1155/2012/318214
work_keys_str_mv AT mortezaseddighin approximationsofantieigenvalueandantieigenvaluetypequantities