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On completely hyperexpansive operators


Author: Ameer Athavale
Journal: Proc. Amer. Math. Soc. 124 (1996), 3745-3752
MSC (1991): Primary 47B20; Secondary 47B39
DOI: https://doi.org/10.1090/S0002-9939-96-03609-X
MathSciNet review: 1353373
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Abstract: We introduce and discuss a class of operators, to be referred to as the class of completely hyperexpansive operators, which is in some sense antithetical to the class of contractive subnormals. The new class is intimately related to the theory of negative definite functions on abelian semigroups. The known interplay between positive and negative definite functions from the theory of harmonic analysis on semigroups can be exploited to reveal some interesting connections between subnormals and completely hyperexpansive operators.


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  • [A] J. Agler, Hypercontractions and subnormality. J. Operator Theory 13 (1985), 203-217. MR 86i:47028
  • [At1] A. Athavale, Holomorphic kernels and commuting operators, Trans. Amer. Math. Soc. 304 (1987), 101-110. MR 88m:47039
  • [At2] A. Athavale, Some operator theoretic calculus for positive definite kernels, Proc. Amer. Math. Soc. 112 (1991), 701-708. MR 92j:47050
  • [B-C-R1] C. Berg, J. P. R. Christensen and P. Ressel, Positive definite functions on abelian semigroups, Math. Ann. 223 (1976), 253-274. MR 54:8165
  • [B-C-R2] C. Berg, J. P. R. Christensen and P. Ressel, Harmonic Analysis on Semigroups, Springer-Verlag, New York, 1984. MR 86b:43001
  • [B-S] C. Berger and B. Shaw, Selfcommutators of multicyclic hyponormal operators are always trace class, Bull. Amer. Math. Soc. 79 (1973), 1193-1199. MR 51:11168
  • [Co] J. Conway, The Theory of Subnormal Operators, Amer. Math. Soc., Providence, RI, 1991. MR 92h:47026
  • [R] S. Richter, Invariant subspaces of the Dirichlet shift, J. Reine Angew. Math. 386 (1988), 205-220. MR 89e:47048
  • [S] A. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys No. 13, Amer. Math. Soc., Providence, RI, 1974, pp. 49-128. MR 50:14341
  • [St] J. Stampfli, Which weighted shifts are subnormal? Pacific J. Math. 17 (1966), 367-379. MR 33:1740

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Additional Information

Ameer Athavale
Affiliation: Department of Mathematics, University of Pune, Pune - 411007, India
Email: athavale@math.unipune.ernet.in

DOI: https://doi.org/10.1090/S0002-9939-96-03609-X
Keywords: Positive definite, negative definite, completely monotone, completely alternating, subnormal, completely hyperexpansive
Received by editor(s): May 17, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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