Positivity and Schwarz inequality for Banach -algebras

Positivity and Schwarz inequality for Banach -algebras

We establish the Schwarz inequality for a class of Banach *-algebras, and use it to derive some consequences, for example when a linear map between Banach *-algebras is a Jordan homomorphism. This applies to the class of Banach *-algebras ℓ 1 ( G , A ; α ) arising from C*-dynamical systems ( A , G ,...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2022-04, Vol.26 (2), Article 34
Hauptverfasser: Harti, Rachid El, Pinto, Paulo R.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Calculus of Variations and Optimal Control
Optimization
Dynamical systems
Econometrics
Fourier Analysis
Homomorphisms
Inequality
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
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Beschreibung
Zusammenfassung:We establish the Schwarz inequality for a class of Banach *-algebras, and use it to derive some consequences, for example when a linear map between Banach *-algebras is a Jordan homomorphism. This applies to the class of Banach *-algebras ℓ 1 ( G , A ; α ) arising from C*-dynamical systems ( A , G , α ) with α an action of a discrete group G on a separable C*-algebra A .
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-022-00904-2