Gupta, Rajeev and Kumar, Surjit and Trivedi, Shailesh (2019) VON NEUMANN'S INEQUALITY FOR COMMUTING OPERATOR-VALUED MULTISHIFTS. In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 147 (6). pp. 2599-2608.
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Recently, Hartz proved that every commuting contractive classical multishift with non-zero weights satisfies the matrix-version of von Neumann's inequality. We show that this result does not extend to the class of commuting operator-valued multishifts with invertible operator weights. In fact, we show that if A and B are commuting contractive d-tuples of operators such that B satisfies the matrix-version of von Neumann's inequality and (1,..., 1) is in the algebraic spectrum of B, then the tensor product A circle times B satisfies von Neumann's inequality if and only if A satisfies von Neumann's inequality. We also exhibit several families of operator-valued multishifts for which von Neumann's inequality always holds.
| Item Type: | Journal Article |
|---|---|
| Publication: | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
| Publisher: | AMER MATHEMATICAL SOC |
| Additional Information: | copyright for this article belongs to PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
| Keywords: | Operator-valued multishift; von Neumann's inequality; tensor product |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 12 Mar 2020 10:30 |
| Last Modified: | 12 Mar 2020 10:30 |
| URI: | http://eprints.iisc.ac.in/id/eprint/62865 |
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