Abstract
We ask whether a connection between isometric functional calculus and factorization of linear functionals, known to hold for the case of a single contraction operator, persists in the case of commuting pairs—or, more generally, n-tuples—of contractions. A positive answer has consequences concerning the jointly invariant subspaces of the commuting operators.
Dedicated to the memory of Jörg Eschmeier.
Communicated by Mihai Putinar.
This article is part of the topical collection “Multivariable Operator Theory. The Jörg Eschmeier Memorial” edited by Raul Curto, Michael Hartz and Mihai Putinar.
W. S. Li was supported in part by a grant from the Simons Foundation
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Bercovici, H., Li, W.S. (2023). A Question About Invariant Subspaces and Factorization. In: Albrecht, E., Curto, R., Hartz, M., Putinar, M. (eds) Multivariable Operator Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-50535-5_5
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DOI: https://doi.org/10.1007/978-3-031-50535-5_5
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