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      Specht's invariant and localization of operator tuples

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          Abstract

          The present paper concerns local theory of operator tuples in the Cowen-Douglas class \(\mathcal {B}_n^m(\Omega) \). We start with point-wise localizations to introduce a kind of operator-valued invariants with which a Specht-type classification for unitary equivalence of \(\mathcal {B}_n^m(\Omega) \) is obtained. Further more, we investigate localization of \(\mathcal {B}_n^m(\Omega) \) on analytic sub-manifolds with a tensorial approach to its geometric classification theory where, among other things, the Specht's invariants are related to curvatures of the holomorphic vector bundles associated to \(\mathcal {B}_n^m(\Omega) \).

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          Journal
          27 March 2020
          Article
          2003.12413
          8c250b3f-5f8e-4fd7-8fb3-943fb38e9b26

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          math.FA

          Functional analysis
          Functional analysis

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