Multiplication Operator Semigroups on Banach lattice valued continuous function spaces

2025/10/04 by Tobi David Olabiyi, Olabiyi, Tobi David
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2510.03607

Abstract

We introduce and characterize, on the Banach lattice valued continuous function space, multiplication operators generating strongly continuous multiplication operator semigroups. Our characterization is the generalization of known results for the scalar-valued continuous functions C₀(Ω) vanishing at infinity, on a locally compact (Hausdorff) space Ω, to Banach lattice C₀(Ω, E) of continuous Banach lattice E-valued functions vanishing at infinity.

Citations

• Extrapolation of operator-valued multiplication operators
• Semigroups of Hadamard multipliers on the space of real analytic\n functions
• Eigenvalues and Stability Properties of Multiplication Operators and\n Multiplication Semigroups

Related

• Multiplication Semigroups on Banach Function Spaces
• Matrix multiplication operators on Banach function spaces
• Multiplication operators on vector-valued function spaces
• Recurrent strongly continuous operator families on Banach space
• Eigenvalues and Stability Properties of Multiplication Operators and\n Multiplication Semigroups