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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.
Banach algebras. --- Harmonic analysis. --- Operator theory. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Functional analysis --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras
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Harmonic analysis. Fourier analysis --- Banach algebras. --- Measure algebras. --- Topological groups. --- Groupes topologiques. --- Algèbres de mesures. --- Banach algebras --- Measure algebras --- Topological groups --- Groups, Topological --- Continuous groups --- Algebras, Measure --- Harmonic analysis --- Measure theory --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras
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Mathematical logic --- Théorie des ensembles --- Set theory --- Forcing (Model theory) --- Independence (Mathematics) --- Axiomatic set theory --- Analyse mathématique --- Mathematical analysis --- Théorie des ensembles --- Analyse mathématique
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Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.
Forcing (Model theory) --- Independence (Mathematics) --- Axiomatic set theory. --- Model theory --- Axioms --- Logic, Symbolic and mathematical --- Set theory --- Axiomatic set theory
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Banach spaces. --- Banach algebras. --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Functions of complex variables --- Generalized spaces --- Topology
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Functional analysis --- Algebraic topology --- Banach algebras. --- Measure algebras. --- Semigroups. --- Functional analysis. --- Banach, Algèbres de --- Algèbres de mesures --- Semi-groupes --- Analyse fonctionnelle --- 51 <082.1> --- Mathematics--Series --- Banach, Algèbres de --- Algèbres de mesures --- Banach algebras --- Measure algebras --- Semigroups --- Group theory --- Algebras, Measure --- Harmonic analysis --- Measure theory --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Analyse harmonique (mathématiques)
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