Reflexive Representations and Banach C*-Modules
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AbstractSuppose A is a unital C*-algebra and m:A → B(X) is unital bounded algebra homomorphism where B(X) is the algebra of all operators on a Banach space X. When X is a Hilbert space, a problem of Kadison [9] asks whether m is similar to a *-homomorphism. Haagerup [5] has shown that the answer is positive when m(A) has a cyclic vector or whenever m is completely bounded. We use this to show m(A) is reflexive (Alg Lat m(A) = m(A)−sot) whenever X is a Hilbert space. Our main result is that whenever A is a separable GCR C*-algebra and X is a reflexive Banach space, then m(A) is reflexive.
2017 ◽
Vol 15
(01)
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pp. 1750004
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2005 ◽
Vol 17
(01)
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pp. 1-14
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1989 ◽
Vol 32
(1)
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pp. 98-104
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1972 ◽
Vol 46
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pp. 155-160
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2005 ◽
Vol 71
(1)
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pp. 107-111
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2015 ◽
Vol 12
(07)
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pp. 1550072
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2005 ◽
Vol 133
(07)
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pp. 2045-2050
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2010 ◽
Vol 88
(2)
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pp. 205-230
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2018 ◽
Vol 20
(4)
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