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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On operator ranges


Author: Bhushan L. Wadhwa
Journal: Proc. Amer. Math. Soc. 80 (1980), 653-654
MSC: Primary 47A05; Secondary 47B20
MathSciNet review: 587947
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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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DOI: https://doi.org/10.1090/S0002-9939-1980-0587947-8
Article copyright: © Copyright 1980 American Mathematical Society