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Hilbert Spaces

C*-algebras. --- Banach algebras. --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras

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Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.

C*-algebras. --- Hilbert algebras. --- Algebras, Hilbert --- Functional analysis --- Von Neumann algebras --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Hilbert modules. --- Modules (Algebra) --- C*-algebras --- Hilbert modules --- Algebra

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This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School . The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians. Contents: Selected Applications of Logic to Classification Problem for C*-Algebras (Ilijas Farah); Subcomplete Forcing and L-Forcing (R

Recursion theory. --- Forcing (Model theory) --- C*-algebras. --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Model theory --- Logic, Symbolic and mathematical

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Quantum mechanics. Quantumfield theory --- Algebraic topology --- Mathematical physics --- C*-algebras. --- Quantum theory. --- Mathematical physics. --- C*-algèbres. --- Théorie quantique. --- Physique mathématique. --- C*-algebras --- Quantum theory --- Physical mathematics --- Physics --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics

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This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. The results presented in this book, which is largely inspired and stimulated by the Atiyah-Singer index theorem, should be of interest to graduates and researchers in mathematical physics, differential topology and differential analysis.

C*-algebras --- Elliptic functions --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Algebra. --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Mathematical analysis