scholarly journals C*–algebras Nearly Contained in Type I Algebras

2013 ◽  
Vol 65 (1) ◽  
pp. 52-65
Author(s):  
Erik Christensen ◽  
Allan M. Sinclair ◽  
Roger R. Smith ◽  
Stuart White
Keyword(s):  
Type I ◽  
C Algebras ◽  
Similarity Problem

AbstractIn this paper we consider near inclusions of C*-algebras. We show that if B is a separable type I C*-algebra and A satisfies Kadison's similarity problem, then A is also type I. We then use this to obtain an embedding of A into B.

APPROXIMATELY INNER FLOWS ON SEPARABLE C*-ALGEBRAS

2002 ◽  
Vol 14 (07n08) ◽  
pp. 649-673 ◽  
Author(s):  
AKITAKA KISHIMOTO
Keyword(s):  
Irreducible Representation ◽  
Von Neumann Algebra ◽  
Automorphism Groups ◽  
Unitary Groups ◽  
Type I ◽  
Von Neumann ◽  
C Algebra ◽  
C Algebras ◽  
Inner Automorphism ◽  
Uniformly Continuous

We present two types of result for approximately inner one-parameter automorphism groups (referred to as AI flows hereafter) of separable C*-algebras. First, if there is an irreducible representation π of a separable C*-algebra A such that π(A) does not contain non-zero compact operators, then there is an AI flow α such that π is α-covariant and α is far from uniformly continuous in the sense that α induces a flow on π(A) which has full Connes spectrum. Second, if α is an AI flow on a separable C*-algebra A and π is an α-covariant irreducible representation, then we can choose a sequence (hn) of self-adjoint elements in A such that αt is the limit of inner flows Ad eithn and the sequence π(eithn) of one-parameter unitary groups (referred to as unitary flows hereafter) converges to a unitary flow which implements α in π. This latter result will be extended to cover the case of weakly inner type I representations. In passing we shall also show that if two representations of a separable simple C*-algebra on a separable Hilbert space generate the same von Neumann algebra of type I, then there is an approximately inner automorphism which sends one into the other up to equivalence.

scholarly journals A Continuous Field of Projectionless C*-Algebras

2001 ◽  
Vol 53 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Andrew Dean
Keyword(s):  
Continuous Functions ◽  
Unit Interval ◽  
Type I ◽  
Crossed Products ◽  
Inductive Limits ◽  
Direct Sums ◽  
Matrix Algebras ◽  
C Algebras ◽  
Finite Dimensional ◽  
Continuous Field

AbstractWe use some results about stable relations to show that some of the simple, stable, projectionless crossed products of O2 by considered by Kishimoto and Kumjian are inductive limits of type C*-algebras. The type I C*-algebras that arise are pullbacks of finite direct sums of matrix algebras over the continuous functions on the unit interval by finite dimensional C*-algebras.

The regular completion of a C*-algebra with large projections

2019 ◽  
Vol 70 (3) ◽  
pp. 999-1007
Author(s):  
Kazuyuki Saitô
Keyword(s):  
Type I ◽  
Wild Type ◽  
C Algebra ◽  
Type Iii ◽  
C Algebras

Abstract When a unital C*-algebra A is prime and has very large projections, it is shown that the regular completion A^ of the algebra A is a simple, wild type III AW*-factor that has no non-zero σ-finite projections. For example, the Weaver algebra, the Crabb algebra and the Katsura algebra are prime C*-algebras that have very large projections. As a corollary, such algebras have no non-zero abelian elements, that is, they are not of type I.

scholarly journals The similarity problem for tensor products of certain C*-algebras

2004 ◽  
Vol 70 (3) ◽  
pp. 385-389 ◽  
Author(s):  
Florin Pop
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
C Algebras ◽  
Similarity Problem ◽  
Bounded Representation

We prove that every bounded representation of the tensor product of two C*-algebras, one of which is nuclear and contains matrices of any order, is similar to a *-representation.

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