Operator of Multiplication by an Analytic Matrix-Valued Function

Abstract

This work can be considered as a supplement to our paper ‘Multiplicity of analytic Toeplitz operators’ [2]. Our aim is to generalize the formula for multiplicity to the matrix case. However the main part of the present paper can be read independently of [2]. We prove that in a certain sense a matrix analytic Toeplitz operator reduces to a scalar operator of multiplication on a space of functions on a Riemann surface. In some cases this reduction provides model within to similarity which resemble that of D.Yakubovich [4]. This reduction, as we hope, may appear useful in other problems concerning matrix Toeplitz operators