Spectral synthesis and operator synthesis
K. Parthasarathy, R. Prakash (2006)
Studia Mathematica
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Relations between spectral synthesis in the Fourier algebra A(G) of a compact group G and the concept of operator synthesis due to Arveson have been studied in the literature. For an A(G)-submodule X of VN(G), X-synthesis in A(G) has been introduced by E. Kaniuth and A. Lau and studied recently by the present authors. To any such X we associate a -submodule X̂ of ℬ(L²(G)) (where is the weak-* Haagerup tensor product ), define the concept of X̂-operator synthesis and prove that a...