Schur Multipliers and Matrix Products
Dan Kucerovsky, Aydin Sarraf
TL;DR
This paper characterizes when Schur multipliers act as algebra homomorphisms, providing conditions for finite and infinite-dimensional cases, and identifying specific forms of Schur matrices that preserve matrix multiplication.
Contribution
It offers necessary and sufficient conditions for Schur maps to be homomorphisms and characterizes Schur matrices that distribute over matrix multiplication.
Findings
Schur multipliers are homomorphisms under specific conditions.
Finite-dimensional Schur matrices that distribute over multiplication have a simple form.
Generalizations to infinite-dimensional cases are established.
Abstract
We give necessary and sufficient conditions for a Schur map to be a homomorphism, with some generalizations to the infinite-dimensional case. In the finite-dimensional case, we find that a Schur multiplier distributes over matrix multiplication if and only if the Schur matrix has a certain simple form.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Advanced Topics in Algebra