Product of matrix valued truncated Toeplitz operators

Abstract

Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication operator to the 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.

Keywords

• model spaces
• truncated Toeplitz operator
• inner function

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