Generalized Crofoot transform and applications

Abstract

Matrix-valued asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These are the generalization of matrix-valued truncated Toeplitz operators. In this article, we describe symbols of matrix-valued asymmetric truncated Toeplitz operators equal to the zero operator. We also use generalized Crofoot transform to find a connection between the symbols of matrix-valued asymmetric truncated Toeplitz operators T(Θ1,Θ2){\mathcal{T}}\left({\Theta }_{1},{\Theta }_{2}) and T(Θ1′,Θ2′){\mathcal{T}}\left({\Theta }_{1}^{^{\prime} },{\Theta }_{2}^{^{\prime} }).

Keywords

• generalized crofoot transform
• matrix-valued truncated toeplitz operators
• matrix-valued asymmetric truncated toeplitz operators
• primary 47b35
• 47a45
• secondary 47b32
• 30j05