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Journal of the London Mathematical Society 2001 64(3):675-689; doi:10.1112/S0024610701002393
© 2001 by London Mathematical Society
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© The London Mathematical Society

A Non-Separable Reflexive Banach Space on Which there are Few Operators

H. M. Wark

39 The Paddock, Perceton, Irvine, Ayrshire KA11 2AZ, james.wark{at}btinternet.com

Received 10 July 2000.

It is shown that there exists a non-separable reflexive Banach space on which every bounded linear operator is the sum of a scalar multiple of the identity operator and an operator of separable range. There is a strong sense that such a Banach space has as few operators as its linear and topological properties allow.


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