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arXiv · 1202.1461

Eigenvalues and Stability Properties of Multiplication Operators and Multiplication Semigroups

Retha Heymann
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Abstract

We investigate uniform, strong, weak and almost weak stability of multiplication semigroups on Banach space valued $L^p$-spaces. We show that, under certain conditions, these properties can be characterized by analogous ones of the pointwise semigroups. Using techniques from selector theory, we prove a spectral mapping theorem for the point spectra of the pointwise and global semigroups and apply this as a major tool for determining almost weak stability.

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Retha Heymann. 2012-02-07. Eigenvalues and Stability Properties of Multiplication Operators and Multiplication Semigroups. https://arxiv.org/abs/1202.1461

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