The maximum unitary rank of some C*-algebras.
The minimal dense two-sided ideal of a C*-algebra with continous trace.
The Order on Projections in C*-Algebras of Real Rank Zero
We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of their lower bounds) decreasing sequences. Under the further assumption that the order is countably downwards closed, we show how to characterize greatest lower bounds of finite collections of projections, and their existence, using the norm and spectrum of simple...
The path space of a higher-rank graph
We construct a locally compact Hausdorff topology on the path space of a finitely aligned k-graph Λ. We identify the boundary-path space ∂Λ as the spectrum of a commutative C*-subalgebra of C*(Λ). Then, using a construction similar to that of Farthing, we construct a finitely aligned k-graph Λ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ∂Λ̃. We show that when Λ is row-finite, we can identify C*(Λ) with a full corner of C*(Λ̃), and deduce that is isomorphic...
The Peripheral Point Spectrum of Schwarz Operators on C*-Algebras.
The primitive ideal space of twisted covariant systems with continuously varying stabilizers.
The real rank of inductive limit C*-algebras.
The Shirali-Ford theorem as a consequence of Ptak theory for hermitian Banach algebras
A simple application of Pták theory for hermitian Banach algebras, combined with a result on normed Q-algebras, gives a non-technical new proof of the Shirali-Ford theorem. A version of this theorem in the setting of non-normed topological algebras is also provided.
The simplicity of the quotient algebra M(A)/A of a simple C*-algebra.
The socle and finite-dimensionality of a semiprime Banach algebra
The space of all bounded operators on Hilbert space does not have the approximation property
The Spectral Radius Formula in Quotient Algebras.
The stable range of C*-algebras.
The strong Morita equivalence for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras
Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional C*-Hopf algebra on a Hilbert C*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras.
The structure of multiplication and addition in simple C*-algebras.
The Structure of the Crossed Product C*-Algebras: A Proof of the Generalized Effros-Hahn Conjecture.
The structure of the Haar systems on locally compact groupoids.
The Theory and Structure of Dual JB-Algebras.
The topological snake lemma and corona algebras.
The trace class is a -algebra.