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  3. Entropy, Compactness and the Approximation of Operators
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 February 2012
    26 October 1990
    ISBN:
    9780511897467
    9780521090940
    DOI:
    https://doi.org/10.1017/CBO9780511897467
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.43kg, 288 Pages
    • Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Cambridge Tracts in Mathematics (98)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Cambridge Tracts in Mathematics (98)
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    Book description

    Entropy quantities are connected with the 'degree of compactness' of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces. The main intention of this Tract is to study the relations between compactness and other analytical properties, e.g. approximability and eigenvalue sequences, of such operators. The authors present many generalized results, some of which have not appeared in the literature before. In the final chapter, the authors demonstrate that, to a certain extent, the geometry of Banach spaces can also be developed on the basis of operator theory. All mathematicians working in functional analysis and operator theory will welcome this work as a reference or for advanced graduate courses.

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