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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Banach space on which there are few operators


Authors: Saharon Shelah and Juris Steprāns
Journal: Proc. Amer. Math. Soc. 104 (1988), 101-105
MSC: Primary 46B99; Secondary 03E05, 05C15, 47B37, 47B99
MathSciNet review: 958051
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Abstract: It is shown that there is a nonseparable Banach space on which every operator has the form $ S + \rho I$ where $ \rho $ is a scalar and $ S$ is an operator with separable range.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0958051-9
Keywords: Nonseparable Banach space, operator with separable range, uncountable cardinal, partition relation
Article copyright: © Copyright 1988 American Mathematical Society