Completely Hyperexpansive Operator Tuples
The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditi...
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| Published in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 3; no. 3; pp. 245 - 257 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Dordrecht
Springer Nature B.V
01.09.1999
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| ISSN: | 1385-1292, 1572-9281 |
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| Abstract | The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy-Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several-variable generalization allows for a stimulating interaction with the multiparameter spectral theory. [PUBLICATION ABSTRACT] |
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| AbstractList | The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy-Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several-variable generalization allows for a stimulating interaction with the multiparameter spectral theory. [PUBLICATION ABSTRACT] |
| Author | Sholapurkar, V.M. Athavale, Ameer |
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| Cites_doi | 10.2307/2374459 10.1090/S0002-9947-1987-0906808-6 10.1090/S0002-9939-96-03609-X 10.1090/surv/013/02 10.1090/surv/036 10.1007/BF01360957 10.1006/jfan.1995.1090 10.1007/978-1-4612-1128-0 10.2307/1968205 |
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| DOI | 10.1023/A:1009719803199 |
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| References | A. Athavale (193958_CR3) 1996; 124 R. E. Curto (193958_CR7) 1981; 266 C. Berg (193958_CR5) 1984 193958_CR6 R. E. Curto (193958_CR10) 1988; 35 R. E. Curto (193958_CR12) 1995; 131 S. Richter (193958_CR15) 1988; 386 J. Agler (193958_CR1) 1985; 13 R. E. Curto (193958_CR8) 1981; 83 R. E. Curto (193958_CR9) 1988 R. E. Curto (193958_CR11) 1985; 107 F. H. Vasilescu (193958_CR18) 1982 A. Athavale (193958_CR2) 1987; 304 T. H. Hildebrandt (193958_CR13) 1933; 34 193958_CR17 193958_CR16 C. Berg (193958_CR4) 1976; 223 N. Jewell (193958_CR14) 1979; 1 |
| References_xml | – volume: 1 start-page: 207 year: 1979 ident: 193958_CR14 publication-title: J. Operator Theory – volume: 107 start-page: 113 year: 1985 ident: 193958_CR11 publication-title: Amer.J.Math. doi: 10.2307/2374459 – volume: 35 start-page: 1 year: 1988 ident: 193958_CR10 publication-title: Operator Theory: Adv. Appl. – volume: 304 start-page: 101 year: 1987 ident: 193958_CR2 publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1987-0906808-6 – volume: 124 start-page: 3745 year: 1996 ident: 193958_CR3 publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-96-03609-X – volume: 83 start-page: 730 year: 1981 ident: 193958_CR8 publication-title: Proc. Amer. Math.Soc. – ident: 193958_CR16 doi: 10.1090/surv/013/02 – ident: 193958_CR6 doi: 10.1090/surv/036 – ident: 193958_CR17 – volume: 223 start-page: 253 year: 1976 ident: 193958_CR4 publication-title: Math. Ann. doi: 10.1007/BF01360957 – volume-title: Math. and its Appl., East European Series year: 1982 ident: 193958_CR18 – volume: 266 start-page: 129 year: 1981 ident: 193958_CR7 publication-title: Trans. Amer. Math. Soc. – volume-title: Pitman Research Notes in Mathematics Series year: 1988 ident: 193958_CR9 – volume: 131 start-page: 279 year: 1995 ident: 193958_CR12 publication-title: J. Funct. Anal. doi: 10.1006/jfan.1995.1090 – volume: 13 start-page: 203 year: 1985 ident: 193958_CR1 publication-title: J. Operator Theory – volume-title: Harmonic Analysis of Semigroups year: 1984 ident: 193958_CR5 doi: 10.1007/978-1-4612-1128-0 – volume: 34 start-page: 317 year: 1933 ident: 193958_CR13 publication-title: Ann. of Math. doi: 10.2307/1968205 – volume: 386 start-page: 205 year: 1988 ident: 193958_CR15 publication-title: J. Reine Angew. Math. |
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| Title | Completely Hyperexpansive Operator Tuples |
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