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A result on hermitian operators

Published online by Cambridge University Press:  18 May 2009

J. E. Jamison  and
Pei-Kee Lin
J. E. Jamison
Affiliation:
Department of Mathematics, Memphis State University, Memphis, Tennessee 38152, U.S.A.
Pei-Kee Lin
Affiliation:
Department of Mathematics, Memphis State University, Memphis, Tennessee 38152, U.S.A.
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Let X be a complex Banach space. For any bounded linear operator T on X, the (spatial) numerical range of T is denned as the set

If V(T) ⊆ R, then T is called hermitian. Vidav and Palmer (see Theorem 6 of [3, p. 78] proved that if the set {H + iK:H and K are hermitian} contains all operators, then X is a Hilbert space. It is natural to ask the following question.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 1 , January 1989 , pp. 71 - 72
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

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