By Harald Upmeier

This booklet hyperlinks of the main energetic examine parts in cutting-edge arithmetic, specifically endless Dimensional Holomorphy (on Banach areas) and the idea of Operator Algebras (C*-Algebras and their non-associative generalizations, the Jordan C*-Algebras). It organizes in a scientific manner a wealth of modern effects that are to date basically available in examine journals and comprises extra unique contributions. utilizing Banach Lie teams and Banach Lie algebras, a concept of transformation teams on endless dimensional manifolds is gifted which covers many very important examples resembling Grassmann manifolds and the unit balls of operator algebras. the speculation additionally has capability significance for mathematical physics through delivering foundations for the development of limitless dimensional curved section areas in quantum box idea.

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