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A note on normal-operator-valued analytic functions


Authors: J. Globevnik and I. Vidav
Journal: Proc. Amer. Math. Soc. 37 (1973), 619-621
MSC: Primary 46L15; Secondary 47B15
DOI: https://doi.org/10.1090/S0002-9939-1973-0310663-0
MathSciNet review: 0310663
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Abstract: In this paper we prove that the set of values of a normal-operator-valued function, defined and analytic on an open connected set in the complex plane, is commutative.


References [Enhancements On Off] (What's this?)

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963. MR 0188745
  • [2] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
  • [3] Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101

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DOI: https://doi.org/10.1090/S0002-9939-1973-0310663-0
Article copyright: © Copyright 1973 American Mathematical Society