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A result on hermitian operators
Published online by Cambridge University Press: 18 May 2009
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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.
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- Copyright © Glasgow Mathematical Journal Trust 1989