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Title: Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space
Author: La Harpe, Pierre de
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1972
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This work is essentially a detailed version of notes published by the author (some in collaboration) in the “Comptes Rendus Hebdomadaires des Séances de l’Académie de Sciences, Série A (Paris)” in 1971 and early 1972 (numbers 272 and 274). The first chapter studies Lie algebras constituted by finite rank operators in a complex Hilbert space, and which correspond in infinite dimensions to the classical simple Lie algebras in finite dimensions. Completions of these with respect to the Schatten uniform crossnorms and to the weak topology provide the Banach-Lie algebras investigated in chapter II. As applications : homogeneous spaces of the corresponding Banach-Lie groups are studied in chapter III; the relationship between cohomologies of the groups, of their Lie algebras and of their classifying spaces is the subject of chapter IV. The main results are: Algebras of derivations, groups of automorphisms, classification of the real forms and cohomological computations for the Lie algebras introduced in chapters I and II. The methods used have been suggested by the theories of finite dimensional semi-simple real and complex Lie algebras, and of associative Banach algebras of linear operators. The results are related to the theory of L*-algebras (Schue, Balachandran) and to the investigations about the Lie structure of simple associative rings (Herstein, Martindale).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics