Symmetric Banach manifolds and Jordan C*-algebras [E-Book] / Harald Upmeier.
Upmeier, Harald,
Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; 1985
Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1 online resource (xii, 444 p.)
englisch
9780444876515
0444876510
Notas de matematica ; 96
North-Holland mathematics studies ; 104
Full Text
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.