Curvature invariant on noncommutative polyballs
Copyright policy )Curvature invariant on noncommutative polyballs
In this paper we develop a theory of curvature (resp. multiplicity) invariant for tensor products of full Fock spaces and also for tensor products of symmetric Fock spaces. This is an attempt to find a more general framework for these invariants and extend some of the results obtained by Arveson for the symmetric Fock space, by the author and Kribs for the full Fock space, and by Fang for the Hardy space over the polydisc. To prove the existence of the curvature and its basic properties in these settings requires a new approach based on noncommutative Berezin transforms and multivariable operator theory on polyballs and varieties, as well as summability results for completely positive maps. The results are presented in the more general setting of regular polyballs.
revised version to appear in Adv. Math
- The University of Texas at San Antonio United States
Invariant subspaces of linear operators, Functional analysis techniques applied to functions of several complex variables, Mathematics - Complex Variables, Several-variable operator theory (spectral, Fredholm, etc.), Mathematics - Operator Algebras, noncommutative polyball, Noncommutative function spaces, Fock space, Functional Analysis (math.FA), Berezin transform, Mathematics - Functional Analysis, characteristic function, FOS: Mathematics, multiplicity invariant, Complex Variables (math.CV), creation operators, invariant subspaces, Operator Algebras (math.OA), curvature invariant
Invariant subspaces of linear operators, Functional analysis techniques applied to functions of several complex variables, Mathematics - Complex Variables, Several-variable operator theory (spectral, Fredholm, etc.), Mathematics - Operator Algebras, noncommutative polyball, Noncommutative function spaces, Fock space, Functional Analysis (math.FA), Berezin transform, Mathematics - Functional Analysis, characteristic function, FOS: Mathematics, multiplicity invariant, Complex Variables (math.CV), creation operators, invariant subspaces, Operator Algebras (math.OA), curvature invariant
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