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A characterization of real and complex Hilbert spaces among all normed spaces

Published online by Cambridge University Press:  17 April 2009

J. Vukman
J. Vukman
Affiliation:
University of Maribor, Veks, Razlagova 14, 62000 Maribor, Yugoslavia.
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Abstract

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Let X be a real or complex normed space and L(X) the algebra of all bounded linear operators on X. Suppose there exists a *-algebra B(X) ⊂ L(X) which contains the identity operator I and all bounded linear operators with finite-dimensional range. The main result is: if each operator U ∈ B(X) with the property U*U = UU* = I has norm one then X is a Hilbert space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 339 - 345
Copyright
Copyright © Australian Mathematical Society 1983

References

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