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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 closed set E in G is of X-synthesis if and only if is of X̂-operator synthesis.
K. Parthasarathy, and R. Prakash. "Spectral synthesis and operator synthesis." Studia Mathematica 177.2 (2006): 173-181. <http://eudml.org/doc/285161>.
@article{K2006, abstract = {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.}, author = {K. Parthasarathy, R. Prakash}, journal = {Studia Mathematica}, keywords = {Spectral synthesis and operator synthesis}, language = {eng}, number = {2}, pages = {173-181}, title = {Spectral synthesis and operator synthesis}, url = {http://eudml.org/doc/285161}, volume = {177}, year = {2006}, }
TY - JOUR AU - K. Parthasarathy AU - R. Prakash TI - Spectral synthesis and operator synthesis JO - Studia Mathematica PY - 2006 VL - 177 IS - 2 SP - 173 EP - 181 AB - 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. LA - eng KW - Spectral synthesis and operator synthesis UR - http://eudml.org/doc/285161 ER -