Kernels of vector-valued Toeplitz operators
Chevrot Nicolas

TL;DR
This paper generalizes the characterization of kernels of Toeplitz operators and nearly $S^*$-invariant subspaces from scalar to vector-valued Hardy spaces, linking operator symbols with subspace structures.
Contribution
It extends Sarason's and Hayashi's results to vector-valued settings, providing new insights into the structure of vector-valued Toeplitz kernels.
Findings
Generalization of scalar results to vector-valued Hardy spaces
Characterization of isometric multiplication operators in vector-valued context
New links between Toeplitz symbols and subspace structures in vector spaces
Abstract
Let be the shift operator on the Hardy space and let be its adjoint. A closed subspace of is said to be nearly -invariant if every element with satisfies . In particular, the kernels of Toeplitz operators are nearly -invariant subspaces. Hitt gave the description of these subspaces. They are of the form with and inner, . A very particular fact is that the operator of multiplication by acts as an isometry on . Sarason obtained a characterization of the functions which act isometrically on . Hayashi obtained the link between the symbol of a Toeplitz operator and the functions and to ensure that a given subspace is the kernel of . Chalendar, Chevrot and Partington studied the nearly…
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Meromorphic and Entire Functions
