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CLASSES OF SEQUENTIALLY LIMITED OPERATORS

Part of: Topological linear spaces and related structures Special classes of linear operators

Published online by Cambridge University Press:  22 July 2015

JAN H. FOURIE  and
ELROY D. ZEEKOEI
JAN H. FOURIE
Affiliation:
Unit for Business Mathematics and Informatics, North-West University(NWU), Private Bag X6001, Potchefstroom 2520, South Africa e-mail: [email protected]; [email protected]
ELROY D. ZEEKOEI
Affiliation:
Unit for Business Mathematics and Informatics, North-West University(NWU), Private Bag X6001, Potchefstroom 2520, South Africa e-mail: [email protected]; [email protected]
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Abstract

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The purpose of this paper is to present a brief discussion of both the normed space of operator p-summable sequences in a Banach space and the normed space of sequentially p-limited operators. The focus is on proving that the vector space of all operator p-summable sequences in a Banach space is a Banach space itself and that the class of sequentially p-limited operators is a Banach operator ideal with respect to a suitable ideal norm- and to discuss some other properties and multiplication results of related classes of operators. These results are shown to fit into a general discussion of operator [Y,p]-summable sequences and relevant operator ideals.

MSC classification

Primary: 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
Secondary: 46A45: Sequence spaces (including Köthe sequence spaces)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 573 - 586
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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