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  3. Introduction to Banach Algebras, Operators, and Harmonic Analysis
  • Cited by 29
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2009
      November 2003
      ISBN:
      9780511615429
      9780521828932
      9780521535847
      DOI:
      https://doi.org/10.1017/CBO9780511615429
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.6kg, 336 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.476kg, 336 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      London Mathematical Society Student Texts (57)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    London Mathematical Society Student Texts (57)
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    Book description

    This work has arisen from lecture courses given by the authors on important topics within functional analysis. The authors, who are all leading researchers, give introductions to their subjects at a level ideal for beginning graduate students, and others interested in the subject. The collection has been carefully edited so as to form a coherent and accessible introduction to current research topics. The first chapter by Professor Dales introduces the general theory of Banach algebras, which serves as a background to the remaining material. Dr Willis then studies a centrally important Banach algebra, the group algebra of a locally compact group. The remaining chapters are devoted to Banach algebras of operators on Banach spaces: Professor Eschmeier gives all the background for the exciting topic of invariant subspaces of operators, and discusses some key open problems; Dr Laursen and Professor Aiena discuss local spectral theory for operators, leading into Fredholm theory.

    Reviews

    'In view of the book's genesis, it is clear that it is quite heterogeneous … This heterogeneity, however, turns out to be one of the volume's strengths: it presents five concise introductions to important parts of functional analysis, each of which conveys its author's outlook on the field … It will certainly be quite useful for new graduate students as well as for non-specialists in the areas covered who want to get a quick overview before delving into dautingly thick treatises as the one by [H. G. Dales ['Banach algebras and automatic continuity', Lond. Math. Soc. Monographs. New Series 24 (2000; Zbl 981.46043)] (on Banach algebras) or K. B. Laursen and M. M. Neumann …'.

    Source: Zentralblatt MATH

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