Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Quotients of Fourier algebras, and representations which are not completely bounded
AU - Choi, Yemon
AU - Samei, Ebrahim
PY - 2013/3/20
Y1 - 2013/3/20
N2 - We observe that for a large class of non-amenable groups G, one can find bounded representations of A(G) on a Hilbert space which are not completely bounded. We also consider restriction algebras obtained from A(G), equipped with the natural operator space structure, and ask whether such algebras can be completely isomorphic to operator algebras. Partial results are obtained using a modified notion of the Helson set which takes into account operator space structure. In particular, we show that when G is virtually abelian and E is a closed subset, the restriction algebra AG(E) is completely isomorphic to an operator algebra if and only if E is finite.
AB - We observe that for a large class of non-amenable groups G, one can find bounded representations of A(G) on a Hilbert space which are not completely bounded. We also consider restriction algebras obtained from A(G), equipped with the natural operator space structure, and ask whether such algebras can be completely isomorphic to operator algebras. Partial results are obtained using a modified notion of the Helson set which takes into account operator space structure. In particular, we show that when G is virtually abelian and E is a closed subset, the restriction algebra AG(E) is completely isomorphic to an operator algebra if and only if E is finite.
U2 - 10.1090/S0002-9939-2013-11974-X
DO - 10.1090/S0002-9939-2013-11974-X
M3 - Journal article
VL - 141
SP - 2379
EP - 2388
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 7
ER -