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Proceedings of the American Mathematical Society

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Jointly quasinormal isometries


Authors: Mary Embry-Wardrop and Richard J. Fleming
Journal: Proc. Amer. Math. Soc. 97 (1986), 463-464
MSC: Primary 47B20; Secondary 47A56
DOI: https://doi.org/10.1090/S0002-9939-1986-0840630-9
MathSciNet review: 840630
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Abstract: If $ U$ and $ V$ are isometries each of which commutes with $ {U^*}V$ and $ {V^*}U$, then a necessary and sufficient condition that $ U$ and $ V$ commute is that the ranges of $ U$ and $ V$ are equal. This result leads to the construction of a subnormal-valued analytic function which has no normal extension.


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

  • [1] R. J. Fleming and J. E. Jamison, Commutative ranges of analytic functions in Banach space, Proc. Amer. Math. Soc. 93 (1985), 48-59. MR 766525 (86b:46076)
  • [2] J. Globevnik and I. Vidav, A note on normal-operator-valued analytic functions, Proc. Amer. Math. Soc. 37 (1973), 619-621. MR 0310663 (46:9761)
  • [3] P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 0208368 (34:8178)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0840630-9
Article copyright: © Copyright 1986 American Mathematical Society

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