Conditions on an operator implying 𝑅𝑒𝜎(𝑇)=𝜎(𝑅𝑒𝑇)

Berberian, S. K.

doi:10.1090/S0002-9947-1971-0270185-5

Conditions on an operator implying $\textrm {Re} \sigma (T)=\sigma (\textrm {Re} T)$
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by S. K. Berberian PDF

Trans. Amer. Math. Soc. 154 (1971), 267-272 Request permission

Abstract:

It is shown that the equation of the title is valid for certain classes of not necessarily normal operators (including Toeplitz operators, and operators whose spectrum is a spectral set), and a new proof is given of C. R. Putnam’s theorem that it is valid for seminormal operators.

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