On vector-valued characters for noncommutative function algebras
| Autor: | Louis E. Labuschagne, David P. Blecher |
|---|---|
| Přispěvatelé: | 22982477 - Labuschagne, Louis Ernst |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Trace (linear algebra) Noncommutative function theory FOS: Physical sciences 01 natural sciences von Neumann algebra symbols.namesake Extension of linear map 0103 physical sciences FOS: Mathematics 0101 mathematics Operator Algebras (math.OA) Mathematical Physics Mathematics Conditional expectation Mathematics::Operator Algebras Applied Mathematics 010102 general mathematics Subalgebra Mathematics - Operator Algebras Jensen inequality Hilbert space Operator algebra Mathematical Physics (math-ph) Operator theory Noncommutative geometry Functional Analysis (math.FA) Mathematics - Functional Analysis Computational Mathematics Computational Theory and Mathematics Von Neumann algebra Jensen measure symbols 010307 mathematical physics Jensen's inequality Gleason parts |
| DOI: | 10.48550/arxiv.1901.02516 |
| Popis: | Let A be a closed subalgebra of a C*-algebra, that is a closed algebra of Hilbert space operators. We generalize to such operator algebras $A$ several key theorems and concepts from the theory of classical function algebras. In particular we consider several problems that arise when generalizing classical function algebra results involving characters ((contractive) homomorphisms into the scalars) on the algebra. For example, the Jensen inequality, the related Bishop-Ito-Schreiber theorem, and the theory of Gleason parts. We will usually replace characters (classical function algebra case) by D-characters, certain completely contractive homomorphisms $\Phi : A \to D$, where D is a C*-subalgebra of A. We also consider some D-valued variants of the classical Gleason-Whitney theorem. Comment: 26 pages, to appear |
| Databáze: | OpenAIRE |
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