Ghara, S and Misra, G (2020) Decomposition of the Tensor Product of Two Hilbert Modules. [Book Chapter]
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Abstract
Given a pair of positive real numbers and a sesqui-analytic function K on a bounded domain in this paper, we investigate the properties of the sesqui-analytic function taking values in m matrices. One of the key findings is that is non-negative definite whenever and are non-negative definite. In this case, a realization of the Hilbert module determined by the is obtained. Let be two Hilbert modules over the polynomial ring Then acts naturally on the tensor product The restriction of this action to the polynomial ring zm] obtained using the restriction map leads to a natural decomposition of the tensor product which is investigated. Two of the initial pieces in this decomposition are identified. © 2020, Springer Nature Switzerland AG.
| Item Type: | Book Chapter |
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| Publication: | Operator Theory: Advances and Applications |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Cowen-Douglas class; Hilbert modules; Jet construction; Non negative definite kernels; Tensor product |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 23 Jan 2023 10:01 |
| Last Modified: | 23 Jan 2023 10:01 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79260 |
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