Banach *-algebra representation
The set of all representations of on a Hilbert space is denoted .
Special kinds of representations:
A representation is said to be topologically irreducible (or just ) if the only closed -invariant of are the trivial ones, and .
A representation is said to be algebrically irreducible if the only -invariant of (not necessarily closed) are the trivial ones, and .
Given two representations and , the of and is the representation given by .
A representation is said to be if there exists a vector such that the set
is dense (http://planetmath.org/Dense) in . Such a vector is called a cyclic vector for the representation .
Linked file: http://aux.planetmath.org/files/objects/9843/BanachAlgebraRepresentation.pdf
|Title||Banach *-algebra representation|
|Date of creation||2013-03-22 17:27:37|
|Last modified on||2013-03-22 17:27:37|
|Last modified by||asteroid (17536)|
|Defines||direct sum of representations|