The irreducibility of C*-algebras acting on Hilbert C*-modules | Zendy

Runliang Jiang | Zendy

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The irreducibility of C*-algebras acting on Hilbert C*-modules

Author(s) -

Runliang Jiang

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1609425j

Subject(s) - mathematics , irreducibility , hilbert space , subalgebra , counterexample , pure mathematics , hilbert–poincaré series , zero (linguistics) , set (abstract data type) , algebra over a field , discrete mathematics , linguistics , philosophy , computer science , programming language

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 full Hilbert B-modules, 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.

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