Analysis now / Gert K. Pedersen

Auteur: Pedersen, Gert Kjærgard (1940-2004) - AuteurType de document: MonographieCollection: Graduate texts in mathematics ; 118Langue: anglaisPays: Allemagne, Etats UnisÉditeur: Berlin : Springer-Verlag, cop. 1989Description: 1 vol. ( XIV-277 p.) ; 24 cm ISBN: 3540967885 ; rel. Résumé: Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view. (Source : Springer).Bibliographie: Bibliogr. p. 267-270. Index. Sujets MSC: 46-02 Functional analysis -- Research exposition (monographs, survey articles)
46B03 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Isomorphic theory (including renorming) of Banach spaces
47B25 Operator theory -- Special classes of linear operators -- Symmetric and selfadjoint operators (unbounded)
46C05 Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Hilbert and pre-Hilbert spaces: geometry and topology
47B10 Operator theory -- Special classes of linear operators -- Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.)
46E30 Functional analysis -- Linear function spaces and their duals -- Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
28A25 Measure and integration -- Classical measure theory -- Integration with respect to measures and other set functions
En-ligne: Springerlink
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Bibliogr. p. 267-270. Index

Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view. (Source : Springer)

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