Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory Paperback / softback
by Raul E. Curto, In Sung Hwang, Woo Young Lee
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
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.
Information
-
Out of stock
- Format:Paperback / softback
- Pages:100 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2019
- Category:
- ISBN:9781470436247
Information
-
Out of stock
- Format:Paperback / softback
- Pages:100 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2019
- Category:
- ISBN:9781470436247
