Functional calculus for m-isometries and related operators on Hilbert spaces and Banach spaces

被引：11
作者：
Gu C. [1 ]
机构：
[1] Department of Mathematics, California Polytechnic State University, San Luis Obispo, 93407, CA
来源：
Acta Scientiarum Mathematicarum | 2015年 / 81卷 / 3-4期
关键词：
(m; Banach space; Functional calculus; Hypercontraction; Hyperexpansion; Isometry; p)-Isometry;
D O I：
10.14232/actasm-014-550-3
中图分类号：
学科分类号：
摘要：
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 Bermúdez, Mendoza and Martinón [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. © 2015 Bolyai Institute, University of Szeged.
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页码：605 / 641
页数：36
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