Closable Multipliers
V.S. Shulman, I.G. Todorov, L.Turowska

TL;DR
This paper investigates the properties of measurable Schur multipliers, focusing on their closability in different topologies, and explores special cases like Toeplitz functions and divided differences, linking them to harmonic analysis and operator theory.
Contribution
It provides a characterization of w*-closable multipliers, relates norm closability to operator synthesis, and studies special multiplier types with concrete examples.
Findings
Characterization of w*-closable multipliers
Relation of Toeplitz multipliers to Fourier algebra
Connection between divided differences and operator smoothness
Abstract
Let (X,m) and (Y,n) be standard measure spaces. A function f in is called a (measurable) Schur multiplier if the map , defined on the space of Hilbert-Schmidt operators from to by multiplying their integral kernels by f, is bounded in the operator norm. The paper studies measurable functions f for which is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if f is of Toeplitz type, that is, if f(x,y)=h(x-y), x,y in G, where G is a locally compact abelian group, then the closability of f is related to the local inclusion of h in the Fourier algebra A(G) of G. If f is a divided difference, that is, a function of the form…
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Taxonomy
TopicsCellular Automata and Applications · Evolutionary Algorithms and Applications
