Geodesic
Reflexive Representations and Banach C*-Modules
Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 443-447

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Suppose 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.
DOI : 10.4153/CMB-1997-052-5
Mots-clés : Primary: 47D30, Secondary, 46L99 
Hadwin, Don; Orhon, Mehmet. Reflexive Representations and Banach C*-Modules. Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 443-447. doi: 10.4153/CMB-1997-052-5
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     title = {Reflexive {Representations} and {Banach} {C*-Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {443--447},
     year = {1997},
     volume = {40},
     number = {4},
     doi = {10.4153/CMB-1997-052-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-052-5/}
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