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On majorizing and cone-absolutely summing mappings

Published online by Cambridge University Press:  09 April 2009

Yau-Chuen Wong
Yau-Chuen Wong
Affiliation:
Department of Mathematics, United College, The Chinese University of Hong Kong Shatin, N.T. Hong Kong
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Abstract

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The notions of majorizing mappings and cone-absolutely summing mappings are studied in the locally convex Riesz space setting. It is shown that a locally convex Riesz space Y is an M-space in the sense of Jameson (1970) if and only if, for any locally convex space E, every continuous linear map from E into Y is majorizing. Another purpose of this note is to study the lattice properties of the vector space ℒl(X, Y) of cone-absolutely summing mappings from one locally convex Riesz space into another Y. It is shown that if Y is both locally and boundedly order complete, then ℒl(X, Y) is an l-ideal in Lb(X, Y). This improves a result of Krengel.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 245 - 251
Copyright
Copyright © Australian Mathematical Society 1977

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