Symbols of truncated Toeplitz operators

Abstract

We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3) factorizations of pseudocontinuable functions from $H^1$. These problems turn out to be closely connected and even, in a sense, equivalent. The new approach based on the factorizations allows us to answer a number of challenging questions about truncated Toeplitz operators posed by Donald Sarason.

19 pages

References in corpus (2)

• Compact embeddings of model subspaces of the Hardy space
• Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators

Cited by in corpus (10)

• Duality theorems for coinvariant subspaces of $H^1$
• Fredholmness and compactness of truncated Toeplitz and Hankel operators
• Nearly invariant subspaces with applications to truncated Toeplitz operators
• An inverse problem for weighted Paley-Wiener spaces
• A survey on reverse Carleson measures
• A Characterization of One-component Inner Functions
• Product of Matrix Valued Truncated Toeplitz Operators
• Sampling measures, Muckenhoupt Hamiltonians, and triangular factorization
• Matrix valued truncated Toeplitz operators: basic properties
• Operators invariant relative to a completely nonunitary contraction