Spectral synthesis and 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 -