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This book links two of the most active research areas in present day mathematics, namely Infinite Dimensional Holomorphy (on Banach spaces) and the theory of Operator Algebras (C*-Algebras and their non-associative generalizations, the Jordan C*-Algebras). It organizes in a systematic way a wealth of recent results which are so far only accessible in research journals and contains additional original contributions. Using Banach Lie groups and Banach Lie algebras, a theory of transformation groups on infinite dimensional manifolds is presented which covers many important examples such as Grassmann manifolds and the unit balls of operator algebras. The theory also has potential importance for mathematical physics by providing foundations for the construction of infinite dimensional curved phase spaces in quantum field theory.

Analytical topology --- Analytical spaces --- Banach manifolds --- C*-algebras --- Jordan algebras

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Johannes snickare --- Jordan målare, --- Criticism and interpretation --- Östra Ryds kyrka (Sweden) --- Jordan malare --- -Johannes snickare --- -Criticism and interpretation --- Ostra Ryds kyrka (Ostra Ryd, Sweden) --- Östra Ryd (Church : Östra Ryd, Sweden) --- Östra Ryds kirka (Östra Ryd, Sweden) --- Jordan målare, --- Östra Ryds kyrka (Sweden)

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This book links two of the most active research areas in present day mathematics, namely Infinite Dimensional Holomorphy (on Banach spaces) and the theory of Operator Algebras (C*-Algebras and their non-associative generalizations, the Jordan C*-Algebras). It organizes in a systematic way a wealth of recent results which are so far only accessible in research journals and contains additional original contributions. Using Banach Lie groups and Banach Lie algebras, a theory of transformation groups on infinite dimensional manifolds is presented which covers many important e

Analytical topology --- Analytical spaces --- Banach manifolds. --- Jordan algebras. --- C*-algebras. --- Banach manifolds --- C*-algebras --- Jordan algebras --- 517.986 --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Algebra, Abstract --- Algebras, Linear --- Manifolds, Banach --- Banach spaces --- Manifolds (Mathematics) --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras

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History of Asia --- anno 1900-1999 --- Israel --- Palestine --- 341.324 <=922> --- Palestinian Arabs --- -327.58 <569.4> --- 852 Internationale conflicten --- 883.4 West-Azië --- Arab Palestinians --- Arabs --- Arabs in Palestine --- Palestinians --- Ethnology --- Bezetting van grondgebied. Opeising van goederen. Opeising van werknemers. Oorlogsbuit--Palestijnen --- West Bank --- -Gaza Strip --- -Qiṭāʻ Ghazzah --- Retsuʻat ʻAzah --- Ḍaffah al-Gharbīyah --- Gadah ha-maʻaravit --- Judaea and Samaria --- Judea and Samaria --- West Bank of the Jordan River --- Yehudah ṿeha-Shomron --- Ethnic relations. --- Ethnic relations --- -Ethnic relations. --- 341.324 <=922> Bezetting van grondgebied. Opeising van goederen. Opeising van werknemers. Oorlogsbuit--Palestijnen --- 327.58 <569.4> --- Arabs in Israel --- Israeli Arabs --- Gaza Strip --- Qiṭāʻ Ghazzah

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This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing.Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Algebraic geometry --- Differential geometry. Global analysis --- Link theory. --- Curves, Plane. --- SINGULARITIES (Mathematics) --- Curves, Plane --- Invariants --- Link theory --- Singularities (Mathematics) --- Geometry, Algebraic --- Low-dimensional topology --- Piecewise linear topology --- Higher plane curves --- Plane curves --- Invariants. --- 3-sphere. --- Alexander Grothendieck. --- Alexander polynomial. --- Algebraic curve. --- Algebraic equation. --- Algebraic geometry. --- Algebraic surface. --- Algorithm. --- Ambient space. --- Analytic function. --- Approximation. --- Big O notation. --- Call graph. --- Cartesian coordinate system. --- Characteristic polynomial. --- Closed-form expression. --- Cohomology. --- Computation. --- Conjecture. --- Connected sum. --- Contradiction. --- Coprime integers. --- Corollary. --- Curve. --- Cyclic group. --- Determinant. --- Diagram (category theory). --- Diffeomorphism. --- Dimension. --- Disjoint union. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence class. --- Euler number. --- Existential quantification. --- Exterior (topology). --- Fiber bundle. --- Fibration. --- Foliation. --- Fundamental group. --- Geometry. --- Graph (discrete mathematics). --- Ground field. --- Homeomorphism. --- Homology sphere. --- Identity matrix. --- Integer matrix. --- Intersection form (4-manifold). --- Isolated point. --- Isolated singularity. --- Jordan normal form. --- Knot theory. --- Mathematical induction. --- Monodromy matrix. --- Monodromy. --- N-sphere. --- Natural transformation. --- Newton polygon. --- Newton's method. --- Normal (geometry). --- Notation. --- Pairwise. --- Parametrization. --- Plane curve. --- Polynomial. --- Power series. --- Projective plane. --- Puiseux series. --- Quantity. --- Rational function. --- Resolution of singularities. --- Riemann sphere. --- Riemann surface. --- Root of unity. --- Scientific notation. --- Seifert surface. --- Set (mathematics). --- Sign (mathematics). --- Solid torus. --- Special case. --- Stereographic projection. --- Submanifold. --- Summation. --- Theorem. --- Three-dimensional space (mathematics). --- Topology. --- Torus knot. --- Torus. --- Tubular neighborhood. --- Unit circle. --- Unit vector. --- Unknot. --- Variable (mathematics).