Baer *-Rings (Paperback) (ISBN-13: 9783662312537)

This book is an elaboration of ideas of Irving Kaplansky introduced in his book Rings of operators ( 52], 54]). The subject of Baer *-rings has its roots in von Neumann's theory of 'rings of operators' (now called von Neumann algebras), that is, *-algebras of operators on a Hilbert space, containing the identity op- ator, that are closed in the weak operator topology (hence also the name W*-algebra). Von Neumann algebras are blessed with an excess of structure-algebraic, geometric, topological-so much, that one can easily obscure, through proof by overkill, what makes a particular theorem work. The urge to axiomatize at least portions of the theory of von N- mann algebras surfaced early, notably in work of S. W. P. Steen 84], I. M. Gel'fand and M. A. Naimark 30], C. E. Rickart 1741, and von Neumann himself 53]. A culmination was reached in Kaplansky's AW*-algebras 47], proposed as a largely algebraic setting for the - trinsic (nonspatial) theory of von Neumann algebras (i. e., the parts of the theory that do not refer to the action of the elements of the algebra on the vectors of a Hilbert space). Other, more algebraic developments had occurred in lattice theory and ring theory. Von Neumann's study of the projection lattices of certain operator algebras led him to introduce continuous geometries (a kind of lattice) and regular rings (which he used to 'coordinatize' certain continuous geometries, in a manner analogous to the introd- tion of division ring coordinates in projective geometry).

Author: Sterling K. Berberian
ISBN-10: 3662312530
ISBN-13: 9783662312537
Publisher: Springer
Language: English
Published: 08/23/2014
Pages: 301
Format: Paperback
Weight: 0.98lbs
Size: 9.21h x 6.14w x 0.66d