Homotonic Algebras
Michael Cwikel, Moshe Goldberg

TL;DR
This paper introduces the concept of homotonic algebras, proves the equivalence of two definitions, and provides a simple inequality to characterize sub-multiplicativity and stability of weighted sup norms within these algebras.
Contribution
It establishes the equivalence of different definitions of homotonicity and offers a straightforward inequality for analyzing norm properties in homotonic algebras.
Findings
Equivalence of two definitions of homotonicity.
A simple inequality characterizing sub-multiplicativity.
Criteria for strong stability of weighted sup norms.
Abstract
An algebra of real or complex valued functions defined on a set shall be called \textit{homotonic} if is closed under forming of absolute values, and for all and in , the product satisfies . Our main purpose in this paper is two-fold: To show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes sub-multiplicativity and strong stability for weighted sup norms on homotonic algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFunctional Equations Stability Results
