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Boundary behavior of vector-valued harmonic functions

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일정 2026-10-16 15:00 ~ 17:00
강연자 황인성 (성균관대학교)
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It is well known that for a Banach space X with the Radon-Nikodým property, the standard Lebesgue space of vector-valued functions is the circle companion of the vector-valued harmonic function space on the unit disk. However, this isometric isomorphism generally fails for operator-valued harmonic spaces because B(X,Y) often lacks the Radon-Nikodým property. In this study, we investigate the boundary behavior of operator-valued harmonic functions to identify their circle companion. Our main result proves that if X is a separable Banach space and Y satisfies the Radon-Nikodým property, then the corresponding Lebesgue space equipped with the strong operator topology is isometrically isomorphic to the space of operator-valued harmonic functions.

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