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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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...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a

Differentiaal"topologie --- Differential topology --- Topologie differentielle --- Topologie différentielle. --- Topologia diferencial. --- Differential topology. --- Topologie différentielle --- Geometry, Differential --- Topology --- Topological algebras. --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra)

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This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how th

Topological algebras. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra)

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About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between qua

Geometric quantization. --- Operator algebras. --- Mathematical physics. --- Physical mathematics --- Physics --- Algebras, Operator --- Operator theory --- Topological algebras --- Geometry, Quantum --- Quantization, Geometric --- Quantum geometry --- Geometry, Differential --- Quantum theory --- Mathematics