On completely hyperexpansive operators
HTML articles powered by AMS MathViewer
- by Ameer Athavale PDF
- Proc. Amer. Math. Soc. 124 (1996), 3745-3752 Request permission
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.References
- Jim Agler, Hypercontractions and subnormality, J. Operator Theory 13 (1985), no. 2, 203–217. MR 775993
- Ameer Athavale, Holomorphic kernels and commuting operators, Trans. Amer. Math. Soc. 304 (1987), no. 1, 101–110. MR 906808, DOI 10.1090/S0002-9947-1987-0906808-6
- Ameer Athavale, Some operator-theoretic calculus for positive definite kernels, Proc. Amer. Math. Soc. 112 (1991), no. 3, 701–708. MR 1068114, DOI 10.1090/S0002-9939-1991-1068114-8
- Christian Berg, Jens Peter Reus Christensen, and Paul Ressel, Positive definite functions on abelian semigroups, Math. Ann. 223 (1976), no. 3, 253–274. MR 420150, DOI 10.1007/BF01360957
- Christian Berg, Jens Peter Reus Christensen, and Paul Ressel, Harmonic analysis on semigroups, Graduate Texts in Mathematics, vol. 100, Springer-Verlag, New York, 1984. Theory of positive definite and related functions. MR 747302, DOI 10.1007/978-1-4612-1128-0
- C. A. Berger and B. I. Shaw, Selfcommutators of multicyclic hyponormal operators are always trace class, Bull. Amer. Math. Soc. 79 (1973), 1193–1199, (1974). MR 374972, DOI 10.1090/S0002-9904-1973-13375-0
- John B. Conway, The theory of subnormal operators, Mathematical Surveys and Monographs, vol. 36, American Mathematical Society, Providence, RI, 1991. MR 1112128, DOI 10.1090/surv/036
- Stefan Richter, Invariant subspaces of the Dirichlet shift, J. Reine Angew. Math. 386 (1988), 205–220. MR 936999, DOI 10.1515/crll.1988.386.205
- Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899
- J. G. Stampfli, Which weighted shifts are subnormal?, Pacific J. Math. 17 (1966), 367–379. MR 193520, DOI 10.2140/pjm.1966.17.367
Additional Information
- Ameer Athavale
- Affiliation: Department of Mathematics, University of Pune, Pune - 411007, India
- Email: athavale@math.unipune.ernet.in
- Received by editor(s): May 17, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- 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