Product of Matrix Valued Truncated Toeplitz Operators
Muhammad Ahsan Khan

TL;DR
This paper investigates conditions under which the product of two matrix valued truncated Toeplitz operators remains within the same class, extending understanding of their algebraic structure in vector-valued function spaces.
Contribution
It provides necessary and sufficient conditions for the product of two matrix valued truncated Toeplitz operators to also be a truncated Toeplitz operator, under certain assumptions.
Findings
Characterization of when the product $A_\Phi A_\Psi$ is a truncated Toeplitz operator.
Extension of scalar results to matrix valued operators.
Conditions depend on properties of the inner function and symbols.
Abstract
Let be a matrix valued truncated Toeplitz operator-the compression of multiplication operator to vector-valued model space , where is a matrix valued non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that the product is itself a matrix valued truncated Toeplitz operator.
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