Functional calculus for ra-isometries and related operators on Hilbert spaces and Banach spaces
We prove that if T is an m-isometry on a Hilbert space and b(z) is an inner function, then b(T) is also an m-isometry. This work is motivated by Bermudez, Mendoza and Martinon [13] where it was proved that if T is an (m, p)-isometry on a Banach space, then Tr is also an (m,p)-isometry for any posit...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2015
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| Sorozat: | Acta scientiarum mathematicarum
81 No. 3-4 |
| Kulcsszavak: | Differenciálegyenlet |
| Tárgyszavak: | |
| mtmt: | http://dx.doi.org/10.14232/actasm-014-550-3 |
| Online Access: | http://acta.bibl.u-szeged.hu/36288 |
| Tartalmi kivonat: | We prove that if T is an m-isometry on a Hilbert space and b(z) is an inner function, then b(T) is also an m-isometry. This work is motivated by Bermudez, Mendoza and Martinon [13] where it was proved that if T is an (m, p)-isometry on a Banach space, then Tr is also an (m,p)-isometry for any positive integer r. We also prove several functional calculus formulas for a single operator or the product of two commuting operators on Hilbert spaces and Banach spaces. Results for classes of operators on Hilbert spaces such as hypercontractions in Agler [1], hyperexpansions in Athavale [7] and alternating hyperexpansion in Sholapurkar and Athavale [41] are obtained by using these formulas. Finally those classes of operators are introduced on Banach spaces. |
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| Terjedelem/Fizikai jellemzők: | 605-641 |
| ISSN: | 0001-6969 |