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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.
Why do elephants play in the mud? Can elephants run as fast as a cheetah? "What Elephants Do" is a story of Lala, the curious young elephant who discovers her own identity during a walk with her mother. Enjoy this beautifully illustrated story with your children and help them discover their unique individuality.
The purpose of love is consciousness. In 1989, lonely and confused art student Insung Hwang expresses his existential angst in a sketch-book that becomes a 22-year diary of unrequited loves. At twenty-three he escapes parental bondage for college only to be trapped by the clutches of religious dogma and self-betrayal. Tormented to find true love he suffers countless rejections, displaces his home and unmasks the yearning for self-importance.
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