multiplicative linear functional
Let be an algebra over .
Multiplicative linear functionals are also called characters of .
Suppose is a commutative Banach algebra over with an identity element. There is a bijective correspondence between the set of maximal ideals in and the set of multiplicative linear functionals in . This correspondence is given by
3 Character space of a Banach algebra
As stated above, the set of all multiplicative linear functionals in a Banach algebra is a locally compact Hausdorff space with the weak-* topology. It becomes a compact set if has an identity element.
Let be a topological space and the algebra of continuous functions . Every point evaluation is a multiplicative linear functional of . In other words, for every point , the function
that gives the evaluation in , is a multiplicative linear functional of .
|Title||multiplicative linear functional|
|Date of creation||2013-03-22 17:22:25|
|Last modified on||2013-03-22 17:22:25|
|Last modified by||asteroid (17536)|
|Synonym||character (of an algebra)|
|Defines||maximal ideal space|