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Eigenvalues and stability properties of multiplication operators and multiplication semigroups
Author(s) -
Heymann Retha
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300046
Subject(s) - mathematics , pointwise , multiplication (music) , eigenvalues and eigenvectors , pure mathematics , banach space , stability (learning theory) , semigroup , pointwise convergence , discrete mathematics , mathematical analysis , combinatorics , physics , quantum mechanics , machine learning , computer science , approx , operating system
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 characterised by analogous ones of the pointwise semigroups. 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.