Eigenvalues and Stability Properties of Multiplication Operators and\n Multiplication Semigroups

2012/02/07 by Retha Heymann, Heymann, Retha · 2 citations
Engineering · Mathematics · #47D06 #Advanced Banach Space Theory #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1202.1461

openalex publication_date 2012/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate uniform, strong, weak and almost weak stability of\nmultiplication semigroups on Banach space valued L^p-spaces. We show that,\nunder certain conditions, these properties can be characterized by analogous\nones of the pointwise semigroups. Using techniques from selector theory, we\nprove a spectral mapping theorem for the point spectra of the pointwise and\nglobal semigroups and apply this as a major tool for determining almost weak\nstability.\n

Cited by

• Multiplication Operator Semigroups on Banach lattice valued continuous function spaces
• Multiplication Semigroups on Banach Function Spaces

Related

• Multiplication Semigroups on Banach Function Spaces
• Stability criteria for positive semigroups on ordered Banach spaces
• Stability criteria for positive semigroups on ordered Banach spaces
• On asymptotics for C₀-semigroups
• Stability estimates for semigroups in the Banach case