{"product_id":"9781470436247","title":"Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory","description":"In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejer Interpolation Problem for matrix rational functions.The authors then extend the $H^\\infty$-functional calculus to an $\\overline{H^\\infty}+H^\\infty$-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of $2\\times 2$ partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.","brand":"Raul E. Curto","offers":[{"title":"Default Title","offer_id":46776562254142,"sku":"9781470436247","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470436247_4a88643c-99d1-41ee-bf9e-6f4bac432e17.jpg?v=1707476989","url":"https:\/\/exclusivebooks.co.za\/products\/9781470436247","provider":"Exclusive Books Online","version":"1.0","type":"link"}