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Operator theory --- 517.982.2 --- Topological linear spaces. Banach spaces. Hilbert spaces. Fre_/chet spaces --- 517.982.2 Topological linear spaces. Banach spaces. Hilbert spaces. Fre_/chet spaces

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This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style is expository and the only prerequisite is a beginner's course on Wormed linear spaces and a minimal knowledge of functional analysis. Thus, Dr Jameson is able to concentrate on important, central results and gives concrete and largely non-technical proofs, often supplying alternative proofs which both contribute something to the understanding. Final-year undergraduates and postgraduates in functional analysis will enjoy this introduction to the subject, and there are many examples and exercises throughout the text to help the reader and to demonstrate the range of application these techniques find. A list of references indicates the way for further reading.

Banach spaces. --- Banach algebras. --- Operator theory. --- Functional analysis --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Functions of complex variables --- Generalized spaces --- Topology --- Espaces linéaires normés. --- Normed linear spaces --- Normed linear spaces. --- Espaces d'operateurs lineaires continus --- Espaces de banach --- Ideaux normes

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This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable fu

Banach spaces. --- Banach, Espaces de --- Banach spaces --- 517.983 --- Functions of complex variables --- Generalized spaces --- Topology --- Linear operators. Linear operator equations --- 517.983 Linear operators. Linear operator equations --- Normed linear spaces. --- Linear normed spaces --- Normed vector spaces --- Functional analysis --- Vector analysis