TY - JOUR
T1 - Completely isometric representations of McbA(G) and UCB(Ĝ)ß
AU - Neufang, Matthias
AU - Ruan, Zhong Jin
AU - Spronk, Nico
PY - 2008/3
Y1 - 2008/3
N2 - Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra McbA(G), which is dual to the representation of the measure algebra M(G), on B(L2(G)). The image algebras of M(G) and M cbA(G) in CBσ(B(L2(G))) are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group G, there is a natural completely isometric representation of UCB(Ĝ)ß on B(L2(G)), which can be regarded as a duality result of Neufang's completely isometric representation theorem for LUC(G)ß.
AB - Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra McbA(G), which is dual to the representation of the measure algebra M(G), on B(L2(G)). The image algebras of M(G) and M cbA(G) in CBσ(B(L2(G))) are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group G, there is a natural completely isometric representation of UCB(Ĝ)ß on B(L2(G)), which can be regarded as a duality result of Neufang's completely isometric representation theorem for LUC(G)ß.
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U2 - 10.1090/S0002-9947-07-03940-2
DO - 10.1090/S0002-9947-07-03940-2
M3 - Article
AN - SCOPUS:77951073938
SN - 0002-9947
VL - 360
SP - 1133
EP - 1161
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 3
ER -