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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