Ultraproducts, $\epsilon$-multipliers, and isomorphisms
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- by Michael Cambern and Krzysztof Jarosz PDF
- Proc. Amer. Math. Soc. 105 (1989), 929-937 Request permission
Abstract:
For a compact Hausdorff space $X$ and Banach dual ${E^ * }$, denote by $C(X,({E^ * },{\sigma ^ * }))$ the Banach space of all continuous functions on $X$ to ${E^ * }$ when the latter space is provided with its weak* topology. We show that if $E_i^ * , i = 1,2$, belong to a class of Banach duals satisfying a condition involving the space of multipliers on $E_i^ *$, then the existence of an isomorphism $T$ mapping $C({X_1},(E_1^ * ,{\sigma ^ * }))$ onto $C({X_2},(E_2^ * ,{\sigma ^ * }))$ with $||T||||{T^{ - 1}}||$ small implies that ${X_1}$ and ${X_2}$ are homeomorphic. Ultraproducts of Banach spaces and the notion of $\varepsilon$-multipliers play key roles in obtaining this result.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 929-937
- MSC: Primary 46E40; Secondary 46B20, 46M99
- DOI: https://doi.org/10.1090/S0002-9939-1989-0965240-7
- MathSciNet review: 965240