Product of Matrix Valued Truncated Toeplitz Operators

Abstract

Let $A_{\Phi }$ be a matrix valued truncated Toeplitz operator-the compression of multiplication operator to vector-valued model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is a matrix valued non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that the product $A_{\Phi }{A}_{\Psi }$ is itself a matrix valued truncated Toeplitz operator.

References in corpus (2)

• Symbols of truncated Toeplitz operators
• Algebras of block Toeplitz matrices with commuting entries