Hausdorff Spectra in functional analysis

I. Tweddle, E. Smirnov

    Research output: Book/ReportBook

    Abstract

    Self-contained, and collating for the first time material that has until now only been published in journals - often in Russian - this book will be of interest to functional analysts, especially those with interests in topological vector spaces, and to algebraists concerned with category theory. The closed graph theorem is one of the corner stones of functional analysis, both as a tool for applications and as an object for research. However, some of the spaces which arise in applications and for which one wants closed graph theorems are not of the type covered by the classical closed graph theorem of Banach or its immediate extensions. To remedy this, mathematicians such as Schwartz and De Wilde (in the West) and Rajkov (in the East) have introduced new ideas which have allowed them to establish closed graph theorems suitable for some of the desired applications. In this book, Professor Smirnov uses category theory to provide a very general framework, including the situations discussed by De Wilde, Rajkov and others. General properties of the spaces involved are discussed and applications are provided in measure theory, global analysis and differential equations.
    LanguageEnglish
    Place of PublicationLondon, England
    PublisherSpringer-Verlag
    Number of pages209
    ISBN (Print)1-85233-571-8
    Publication statusPublished - 2002

    Publication series

    NameSpringer monographs in mathematics
    PublisherSpringer-Verlag

    Fingerprint

    Functional Analysis
    Closed
    Category Theory
    Graph in graph theory
    Theorem
    Algebraist
    Measure Theory
    Global Analysis
    Topological Vector Space
    Stefan Banach
    Differential equation

    Keywords

    • functional analysis
    • Hausdorff Spectra
    • topology
    • numerical mathematics

    Cite this

    Tweddle, I., & Smirnov, E. (2002). Hausdorff Spectra in functional analysis. (Springer monographs in mathematics). London, England: Springer-Verlag.
    Tweddle, I. ; Smirnov, E. / Hausdorff Spectra in functional analysis. London, England : Springer-Verlag, 2002. 209 p. (Springer monographs in mathematics).
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    Tweddle, I & Smirnov, E 2002, Hausdorff Spectra in functional analysis. Springer monographs in mathematics, Springer-Verlag, London, England.

    Hausdorff Spectra in functional analysis. / Tweddle, I.; Smirnov, E.

    London, England : Springer-Verlag, 2002. 209 p. (Springer monographs in mathematics).

    Research output: Book/ReportBook

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    AB - Self-contained, and collating for the first time material that has until now only been published in journals - often in Russian - this book will be of interest to functional analysts, especially those with interests in topological vector spaces, and to algebraists concerned with category theory. The closed graph theorem is one of the corner stones of functional analysis, both as a tool for applications and as an object for research. However, some of the spaces which arise in applications and for which one wants closed graph theorems are not of the type covered by the classical closed graph theorem of Banach or its immediate extensions. To remedy this, mathematicians such as Schwartz and De Wilde (in the West) and Rajkov (in the East) have introduced new ideas which have allowed them to establish closed graph theorems suitable for some of the desired applications. In this book, Professor Smirnov uses category theory to provide a very general framework, including the situations discussed by De Wilde, Rajkov and others. General properties of the spaces involved are discussed and applications are provided in measure theory, global analysis and differential equations.

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    Tweddle I, Smirnov E. Hausdorff Spectra in functional analysis. London, England: Springer-Verlag, 2002. 209 p. (Springer monographs in mathematics).