On operator ranges

Wadhwa, Bhushan L.

doi:10.1090/S0002-9939-1980-0587947-8

On operator ranges
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by Bhushan L. Wadhwa

Proc. Amer. Math. Soc. 80 (1980), 653-654

DOI: https://doi.org/10.1090/S0002-9939-1980-0587947-8

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Abstract:

If f is any vector-valued bounded function defined on open set D of the complex plane, and T is any bounded linear operator on a Hilbert space such that ${\sigma _R}({T^ \ast })$ is empty and if ${(T - zI)^2}f(z) = x$ for all z in D then f is analytic.

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