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Commutants that do not dilate


Author: Douglas N. Clark
Journal: Proc. Amer. Math. Soc. 35 (1972), 483-486
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0303313-X
MathSciNet review: 0303313
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Abstract: The Lifting Theorem deals with dilation of the commutant of an operator $ {T_1}$ on Hilbert space. In this note, counterexamples are given to generalizations of the theorem involving N commuting operators $ {T_1},{T_2}, \cdots ,{T_N}$.


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

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  • [3] D. E. Sarason, Generalized interpolation in $ {H^\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179-203. MR 34 #8193. MR 0208383 (34:8193)
  • [4] B. Sz.-Nagy and C. Foiaş, Commutants de certains opérateurs, Acta. Sci. Math. (Szeged) 29 (1968), 1-17. MR 39 #3346. MR 0242011 (39:3346)
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DOI: https://doi.org/10.1090/S0002-9939-1972-0303313-X
Article copyright: © Copyright 1972 American Mathematical Society

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