Multiplication Operator Semigroups on Banach lattice valued continuous function spaces

Tobi David Olabiyi

Multiplication Operator Semigroups on Banach lattice valued continuous function spaces

Functional Analysis 2025-10-07 v1 Operator Algebras Spectral Theory

Authors: Tobi David Olabiyi

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 $C_0(\Omega)$ vanishing at infinity, on a locally compact (Hausdorff) space $\Omega$ , to Banach lattice $C_0(\Omega, E)$ of continuous Banach lattice $E$ -valued functions vanishing at infinity.

Keywords

operator theory on banach spaces operator semigroups banach space

Cite

@article{arxiv.2510.03607,
  title  = {Multiplication Operator Semigroups on Banach lattice valued continuous function spaces},
  author = {Tobi David Olabiyi},
  journal= {arXiv preprint arXiv:2510.03607},
  year   = {2025}
}

Comments

14 pages

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