Baer *-rings - Grundlehren Der Mathematischen Wissenschaften - Sterling K. Berberian - Libros - Springer-Verlag Berlin and Heidelberg Gm - 9783662312537 - 23 de agosto de 2014
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Sterling K. Berberian
Baer *-rings - Grundlehren Der Mathematischen Wissenschaften Softcover Reprint of the Original 1st Ed. 1972 edition

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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).

314 pages, biography

Medios de comunicación Libros     Paperback Book   (Libro con tapa blanda y lomo encolado)
Publicado 23 de agosto de 2014
Fecha de lanzamiento original 2013
ISBN13 9783662312537
Editores Springer-Verlag Berlin and Heidelberg Gm
Páginas 301
Dimensiones 155 × 235 × 17 mm   ·   444 g
Lengua Inglés  

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