Mackey imprimitivity and commuting tuples of homogeneous normal operators

Misra, G and Narayanan, EK and Varughese, C (2024) Mackey imprimitivity and commuting tuples of homogeneous normal operators. In: Indian Journal of Pure and Applied Mathematics, 55 (03). 1010 -1025.

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Abstract

In this semi-expository article, we investigate the relationship between the imprimitivity introduced by Mackey several decades ago and commuting d- tuples of homogeneous normal operators. The Hahn�Hellinger theorem gives a canonical decomposition of a �- algebra representation � of C0(S) (where S is a locally compact Hausdorff space) into a direct sum. If there is a group G acting transitively on S and is adapted to the �- representation � via a unitary representation U of the group G, in other words, if there is an imprimitivity, then the Hahn�Hellinger decomposition reduces to just one component, and the group representation U becomes an induced representation, which is Mackey�s imprimitivity theorem. We consider the case where a compact topological space S�Cd decomposes into finitely many G- orbits. In such cases, the imprimitivity based on S admits a decomposition as a direct sum of imprimitivities based on these orbits. This decomposition leads to a correspondence with homogeneous normal tuples whose joint spectrum is precisely the closure of G- orbits. © The Indian National Science Academy 2024.

Item Type:	Journal Article
Publication:	Indian Journal of Pure and Applied Mathematics
Publisher:	Indian National Science Academy
Additional Information:	The copyright for this article belongs to Indian National Science Academy.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	20 Dec 2024 04:28
Last Modified:	20 Dec 2024 04:28
URI:	http://eprints.iisc.ac.in/id/eprint/85906

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