The irreducibility of C*-algebras acting on Hilbert C*-modules
Keyword(s):
Let B be a C*-algebra, E be a Hilbert B module and L(E) be the set of adjointable operators on E. Let A be a non-zero C*-subalgebra of L(E). In this paper, some new kinds of irreducibilities of A acting on E are introduced, which are all the generalizations of those associated to Hilbert spaces. The difference between these irreducibilities are illustrated by a number of counterexamples. It is concluded that for a full Hilbert B-module, these irreducibilities are all equivalent if and only if the underlying C*-algebra B is isomorphic to the C*-algebra of all compact operators on a Hilbert space.
1997 ◽
Vol 49
(6)
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pp. 1188-1205
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2016 ◽
Vol 59
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pp. 1-10
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2005 ◽
Vol 79
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pp. 391-398
1991 ◽
Vol 110
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pp. 143-145
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1987 ◽
Vol 29
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pp. 93-97
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2017 ◽
Vol 15
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pp. 1750004
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2002 ◽
Vol 13
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pp. 1009-1025
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