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Isometric Preduals of James Spaces

Published online by Cambridge University Press:  20 November 2018

Leon Brown  and
Takashi Ito
Leon Brown
Affiliation:
Wayne State University, Detroit, Michigan
Takashi Ito
Affiliation:
Wayne State University, Detroit, Michigan
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A Banach space B is called an isometric predual, or simply a predual, of a Banach space X if the dual B* of B is isometrically isomorphic to X. A Banach space X is said to have a unique (isometric) predual if X has a predual and all preduals are mutually isometrically isomorphic. In general a Banach space does not have a unique predual even if it has a predual. A simple example of this is the space l1, because c0 and c are isometric preduals of l1 but not isometrically isomorphic. A. Grothendieck [3] first noticed that L∞-spaces have unique preduals, and then S. Sakai generalized this to von Neumann algebras (see p. 30 of [9]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 59 - 69
Copyright
Copyright © Canadian Mathematical Society 1980

References

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