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Topological algebras --- Topological algebras. --- Algebras, Topological --- topological-algebraic structures --- topological dynamics --- topological semigroups --- noncommutative probability --- fuzzy topological algebras --- Functional analysis --- Linear topological spaces --- Rings (Algebra) --- Calculus

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Fundamentals of the theory of operator algebras. V4

Operator algebras. --- Operator theory. --- Functional analysis --- Algebras, Operator --- Operator theory --- Topological algebras

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Topological algebras

Algebraic topology --- Topological algebras. --- Fonctions continues --- Functions, Continuous --- Topological algebras --- 517.986 --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra) --- Differential topology. --- Geometry, Differential --- Topology --- Algèbres topologiques --- Algèbres topologiques

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This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. Due to its very clear style and the careful organization of the material, this truly brilliant book may serve as an introduction into the field, yet it also provides an excellent source of information on specific topics in spectral theory for the working mathematician. Review of the first edition by M. Grosser, Vienna Monatshefte für Mathematik Vol. 146, No. 1/2005.

Operator theory. --- Banach algebras. --- Functional analysis --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Operator Theory.

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to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. A factor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

Operator algebras --- Algèbres d'opérateurs --- 517.986 --- banachalgebra --- dicht --- tensoren --- integralen --- duaal --- Von Neumann --- poolse ruimte --- c*-algebra --- topologie --- spoor --- borel --- commutant --- Algebras, Operator --- Operator theory --- Topological algebras --- Topological algebras. Theory of infinite-dimensional representations --- Operator algebras. --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Analytical spaces --- Algèbres d'opérateurs --- Operator theory. --- Mathematical physics. --- Operator Theory. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Functional analysis --- Mathematics --- Algèbres topologiques --- Algèbres topologiques. --- Algèbres topologiques.