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Isometric results on a measure of non-compactness for operators on Banach spaces

Published online by Cambridge University Press:  17 April 2009

S. J. Dilworth
S. J. Dilworth
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, United States of America.
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Abstract

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For each λ ≥ 1 a class of Banach spaces φλ is defined. Isometric results are obtained on the equivalence between a measure of non-compactness and the essential norm of a linear operator defined on a φλ space. Best values of λ for the classical Banach spaces and for spaces with unconditional basis are investigated. For the space c of convergent sequences the non-existence of a λ-unconditional basis with λ < 2 is deduced.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 1 , February 1987 , pp. 27 - 33
Copyright
Copyright © Australian Mathematical Society 1987

References

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