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Banach *-algebra representation (Definition)
CyclicVector2

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"Banach *-algebra representation" is owned by asteroid. [ full author list (2) ]
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Also defines:  subrepresentation, cyclic representation, cyclic vector, nondegenerate representation, topologically irreducible, algebrically irreducible, direct sum of representations, unitarily equivalent

Attachments:
representations of Banach *-algebras are continuous (Theorem) by asteroid
criterion for a Banach *-algebra representation to be irreducible (Theorem) by asteroid
topologically irreducible representations are algebrically irreducible for $C^*$-algebras (Theorem) by asteroid
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Cross-references: unitary, direct sum of Hilbert spaces, vectors, linear span, equivalent, operator, invariant, subspace, closed, Hilbert space, bounded operators, *-algebra, *-homomorphism, Banach *-algebra
There are 11 references to this entry.

This is version 17 of Banach *-algebra representation, born on 2007-08-09, modified 2008-11-08.
Object id is 9843, canonical name is BanachAlgebraRepresentation.
Accessed 4266 times total.

Classification:
AMS MSC46H15 (Functional analysis :: Topological algebras, normed rings and algebras, Banach algebras :: Representations of topological algebras)
 46K10 (Functional analysis :: Topological algebras with an involution :: Representations of topological algebras with involution)

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Banach *-algebra representation remark by asteroid on 2008-09-17 19:24:02
To bci1,

I've deleted the remark you added, because the second part of it doesn't really make sense to me.. I'll post it here anyway:

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"Recall that a Hilbert space is a Banach space in the norm induced by the inner product, and also that
a Banach *-algebra is a Banach algebra endowed with an involution (*); as the definition of a Banach
algebra also involves a Banach space with additional algebraic properties, the representation of a
Banach *-algebra on a Hilbert space is natural in the sense that the space underlying such a representation
is a Banach space both for the domain and range (codomain) of the *-homomorphism that defines $\pi$."
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If you tell me what you are trying to say, I can work something out I guess..
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