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The lambda-property for generalised direct sums of normed spaces

Published online by Cambridge University Press:  17 April 2009

Robert H. Lohman  and
Thaddeus J. Shura
Robert H. Lohman
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States of America
Thaddeus J. Shura
Affiliation:
Department of Mathematical Sciences, Kent State University at Salem, Salem OH 44460, United States of America
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This paper considers direct sums of normed spaces with respect to a Banach space with a normalised, unconditionally strictly monotone basis. Necessary and sufficient conditions are given for such direct sums to have the λ-property. These results are used to construct examples of reflexive Banach spaces U and V such that U has the uniform λ-property but U* fails to have the λ-property, while V and V* fail to have the λ-property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 441 - 450
Copyright
Copyright © Australian Mathematical Society 1990

References

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