Jointly quasinormal isometries
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- by Mary Embry-Wardrop and Richard J. Fleming PDF
- Proc. Amer. Math. Soc. 97 (1986), 463-464 Request permission
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
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- J. Globevnik and I. Vidav, A note on normal-operator-valued analytic functions, Proc. Amer. Math. Soc. 37 (1973), 619–621. MR 310663, DOI 10.1090/S0002-9939-1973-0310663-0
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
Additional Information
- © Copyright 1986 American Mathematical Society
- 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