Spectral synthesis and operator synthesis

• Autorzy: K. Parthasarathy , R. Prakash
• Języki publikacji: EN

Abstrakty

EN

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 $V^{∞}(G)$-submodule X̂ of ℬ(L²(G)) (where $V^{∞}(G)$ is the weak-* Haagerup tensor product $L^{∞}(G) ⊗_{w*h} L^{∞}(G)$), define the concept of X̂-operator synthesis and prove that a closed set E in G is of X-synthesis if and only if $E*: = {(x,y) ∈ G × G: xy^{-1} ∈ E}$ is of X̂-operator synthesis.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 177
• Numer: 2
• Strony: 173-181

Daty

wydano

2006

Twórcy

autor

K. Parthasarathy

• Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, India

autor

R. Prakash

• Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai-600 005, India

Identyfikatory

DOI

10.4064/sm177-2-6