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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Holomorphic kernels and commuting operators


Author: Ameer Athavale
Journal: Trans. Amer. Math. Soc. 304 (1987), 101-110
MSC: Primary 47B20; Secondary 47A20
MathSciNet review: 906808
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Abstract: Necessary and sufficient conditions in terms of operator polynomials are obtained for an $ m$-tuple $ T = ({T_1}, \ldots ,{T_m})$ of commuting bounded linear operators on a separable Hilbert space $ \mathcal{H}$ to extend to an $ \dot m$-tuple $ S = ({S_1}, \ldots ,{S_m})$ of operators on some Hilbert space $ \mathcal{K}$, where each $ {S_i}$ is realized as a $ {\ast}$-representation of the adjoint of a multiplication operator on the tensor product of a special type of functional Hilbert spaces. Also, necessary and sufficient conditions in terms of operator polynomials are obtained for $ T$ to have a commuting normal extension.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0906808-6
PII: S 0002-9947(1987)0906808-6
Keywords: Positive definite, regular analytic model atom, kernel, tensor product, commuting normal extension, $ {\ast}$ -dilation
Article copyright: © Copyright 1987 American Mathematical Society