Reduced Spectral Synthesis and Compact Operator Synthesis

V.S. Shulman, Ivan Todorov, Lyudmila Turowska

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We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact group with an open abelian subgroup has a subset that fails reduced spectral synthesis. We introduce compact operator synthesis as an operator algebraic counterpart of this notion and link it to other exceptional sets in operator algebra theory, studied previously. We show that a closed subset E of a second countable locally compact group G satisfies reduced local spectral synthesis if and only if the subset

of satisfies compact operator synthesis. We apply our results to questions about the equivalence of linear operator equations with normal commuting coefficients on Schatten p-classes.
Original languageEnglish
Article number107109
JournalAdvances in Mathematics
Early online date26 Mar 2020
Publication statusPublished - 24 Jun 2020


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