Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Định mức giới hạn của khoản tiền hữu hạn trực tiếp của i_ $ \ infty $ yếu tố. | J. OPERATOR THEORY 15 1986 3-13 Copyright by INCREST 1986 NORM LIMITS OF FINITE DIRECT SUMS OF 1 FACTORS BERNDT BRENKEN Consider unital c -algebras 91 which are direct limits lim 9t p where 9Ĩ I n e N is a sequence of von Neumann algebras each a finite direct sum of countably decomposable type loo factors and where p 9Ĩ - 91 1 is an injective unital homomorphism. Call such an algebra a type loo sequence algebra. Included in this class are the type loo funnels of 9 . The isomorphism classes of these algebras are completely described by the isomorphism classes of monoids associated with the algebras in a manner analogous to the dimension group theory of AF algebras 2 4 5 . In fact the enveloping groups of these monoids are the Ko groups of these algebras however these are zero Ko . 0 for a type IM . For algebras where the maps p are finite embeddings we conclude that the isomorphism classes are described by isomorphism classes of certain dimension groups. The monoid associated with a type Ico sequence algebra has a partial ordering and the ideal structure of the algebra is reflected in the order ideal structure of the partially ordered monoid. Simple conditions involving the semilattice consisting of all idempotents in the monoid distinguish various ideal structures. The countable decomposability of the factors ensures that each embedding q n is normal 6 9 . All representations are on separable Hilbert spaces and all homomorphisms of c -algebras are -homomorphisms. If yf is a Hilbert space will denote the von Neumann algebra of all bounded operators on X Idj will be the identity operator and Idr r e N u will mean Id z for some Hilbert space d of dimension r. By subspace of a Hilbert space we mean closed subspace. Ideals of a c -algebra will be closed and two sided. An automorphism a of a c -algebra is inner if there is a unitary Ư in with a .v ad U x x 6 . If X2 . is a sequence of sets and maps define ipmn p -ỵ . p m n . The author would like to thank
