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Named for Banach, one of the great mathematicians of the twentieth century, the concept of Banach spaces figures prominently in the study of functional analysis with applications to integral and differential equations, approximation theory, harmonic analysis, convex geometry, numerical mathematics, analytic complexity, and probability theory. Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. While other historical texts on the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th century. Banach space theory is presented in a broad mathematical context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, and logic. Equal emphasis is given to both spaces and operators. Numerous examples and counterexamples elucidate the scope of the underlying concepts. As a stimulus for further research, the text also contains many problems which have not been previously solved. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor. Helpful information is also provided for professors preparing their own lectures on functional analysis.
Banach spaces --- Linear operators --- History. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Functions of complex variables --- Generalized spaces --- Topology --- Functional analysis. --- Operator theory. --- History of Mathematical Sciences. --- Functional Analysis. --- Operator Theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics. --- Annals --- Auxiliary sciences of history --- Math --- Science
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Functional analysis --- Operator theory --- Banach spaces --- s-numbers --- Eigenvalues --- #TELE:d.d. Prof. R. Govaerts --- #TELE:SISTA --- Matrices --- Functions of complex variables --- Generalized spaces --- Topology --- Numbers, s --- Number theory --- Banach spaces. --- Eigenvalues. --- Operator theory. --- s-numbers. --- S-numbers. --- Analyse fonctionnelle --- Functional analysis. --- Espaces de banach --- Espaces d'operateurs lineaires continus --- Operateurs lineaires --- Ideaux normes
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Banach spaces - History. --- Linear operators - History. --- Banach spaces --- Linear operators
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Locally convex spaces --- Tensor products --- Linear operators --- Nuclear spaces (Functional analysis)
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Operator theory --- Functional analysis --- Mathematics --- analyse (wiskunde) --- functies (wiskunde) --- geschiedenis --- wiskunde
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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
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