Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2010; 47(5): 899-924

Printed September 1, 2010

https://doi.org/10.4134/JKMS.2010.47.5.899

Copyright © The Korean Mathematical Society.

Averages and compact, absolutely summing and nuclear operators on $C\left(\Omega \right)$

Dumitru Popa

University of Constanta

Abstract

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space $C\left( \Omega \right) $ for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

Keywords: Banach spaces of continuous functions, weakly compact, compact, nuclear, $p$-summing

MSC numbers: 46B28, 47B10, 47G10