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Weakly compact multilinear mappings

Published online by Cambridge University Press:  20 January 2009

Richard M. Aron  and
Pablo Galindo
Richard M. Aron
Affiliation:
Mathematics Department, Kent State University, Kent, Ohio 44242, U.S.A. E-mail: [email protected]
Pablo Galindo
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain, E-mail: [email protected]
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Abstract

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The notion of Arens regularity of a bilinear form on a Banach space E is extended to continuous m-linear forms, in such a way that the natural associated linear mappings, E→L (m−1E) and (m – l)-linear mappings E × … × E → E', are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 181 - 192
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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