On the coincidence of types of a real <i>AW</i> *-algebra and its complexification
S. AlbeverioInstitut für Angewandte Mathematik, Universität Bonn , Bonn, GermanySh. A. AyupovRomanovskii Mathematical Institute of the National Academy of Sciences of the Uzbek Republic, Tashkent, UzbekistanA. Kh. AbduvaitovNational University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan
ABI
Abstract
We consider real AW*-algebras, that is, Kaplansky algebras over the field of real numbers. As in the case of complex von Neumann algebras and complex AW*-algebras, real AW*-algebras are classified in terms of types , , , , and . We prove that if the complexification of a real AW*-algebra A also is an AW*-algebra, then the types of A and M coincide.