Reduced spectral synthesis and compact operator synthesis
Artikel i vetenskaplig tidskrift, 2020

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 with 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 E*={(s,t):ts^{-1}∈E} of G×G 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.

spectral synthesis, operator synthesis, reduced groups C*-algebra, group


I. G. Todorov

Lyudmyla Turowska

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 367 107109


Grundläggande vetenskaper


Matematisk analys



Mer information