Espaces d'interpolation réels : topologie et géométrie / Bernard Beauzamy
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 666Langue : français.Éditeur : Berlin : Springer-Verlag, 1978ISBN: 9783540089230.ISSN: 1617-9692.Sujet MSC : 46M35, Methods of category theory in functional analysis, Abstract interpolation of topological vector spaces46E35, Functional analysis - Linear function spaces and their duals, Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems
46B10, Functional analysis - Normed linear spaces and Banach spaces; Banach lattices, Duality and reflexivity in normed linear and Banach spaces
46B20, Functional analysis - Normed linear spaces and Banach spaces; Banach lattices, Geometry and structure of normed linear spacesEn-ligne : Springerlink | MathSciNet
This is an exposition of some aspects of the theory of real interpolation spaces. It is intended for the reader interested in the geometry of Banach spaces.
The author uses a slightly modified definition of J.-L. Lions and J. Peetre [Inst. Hautes Études Sci. Publ. Math. No. 19 (1964), 5–68; MR0165343 (29 #2627)]. He studies mostly the geometric and linear-topological properties of interpolation spaces. This includes some useful permanence properties (for instance, conditions for uniform convexity of interpolation spaces) as well as a development of the ideas initiated by the factorization theorem for weakly compact operators. The author gives a readable and rather complete presentation of a series of papers which he devoted to this subject. (MathSciNet)
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