Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2017; 32(4): 899-908

Online first article June 22, 2017      Printed October 31, 2017

https://doi.org/10.4134/CKMS.c160253

Copyright © The Korean Mathematical Society.

Fixed points of BSC-sequences

Parviz Sadat Hosseini, Bahmann Yousefi

Payame Noor University, Payame Noor University

Abstract

We call a sequence $(T_n)_n$ of bounded operators on a Banach space X, BSC-Sequence if it is a Cauchy sequence in the strong operator topology and is uniformly bounded below. We determine conditions under which such sequences has a fixed point.

Keywords: orbit of an operator, $J$-sets, $J^{mix} $-sets, $J$-class operator

MSC numbers: 47A65, 47A99

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