Weighted composition operators and locally convex algebras |
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Authors: | Edoardo Vesentini |
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Institution: | 1.Dipartimento di Matematica,Politecnico di Torino,Torino,Italy |
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Abstract: | The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field ? among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A : A→ A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra. |
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