Ideals of $A(G)$ and bimodules over maximal abelian selfadjoint algebras

Abstract

This paper is concerned with weak* closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak* closed subspaces of B(L^2(G)) which are invariant under both Schur multipliers and a canonical action of M(G) on B(L^2(G)) via completely bounded maps. We study the special cases of extremal ideals with a given null set and, for a large class of groups, we establish a link between relative spectral synthesis and relative operator synthesis.

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References in corpus (2)

• Simple Lie groups without the Approximation Property
• Sets of multiplicity and closable multipliers on group algebras

Cited by in corpus (6)

• Ideals of the Fourier algebra, supports and harmonic operators
• Synthetic properties of locally compact groups: preservation and transference
• Bimodules over $\mathrm{VN}(G)$, harmonic operators and the non-commutative Poisson boundary
• Reduced spectral synthesis and compact operator synthesis
• Operator system structures and extensions of Schur multipliers
• Homomorphisms of Fourier algebras and transference results