On the Homomorphic Image of the Center of a C*-Algebra.
On the hyperbolic metric on Harnack parts
On the imbedding of normed rings into the ring of operators in Hilbert space
On the K-theory of the -algebra generated by the left regular representation of an Ore semigroup
We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.
On the linking algebra of Hilbert modules and Morita equivalence of locally -algebras.
On the Moore-Penrose inverse in C*-algebras.
In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra...
On the range of completely bounded maps.
On the reflexivity of pairs of isometries and of tensor products of some operator algebras
On the spectrum of the sum of generators of a finitely generated group, II
On the structure of covers of sofic shifts.
On the Topology of the Spectrum of a C+-Algebra.
On the two-fold symbol chain of a C*-algebra of singular integral operators on a polycylinder.
On weak sequential convergence in JB*-triple duals
We study various Banach space properties of the dual space E* of a homogeneous Banach space (alias, a JB*-triple) E. For example, if all primitive M-ideals of E are maximal, we show that E* has the Alternative Dunford-Pettis property (respectively, the Kadec-Klee property) if and only if all biholomorphic automorphisms of the open unit ball of E are sequentially weakly continuous (respectively, weakly continuous). Those E for which E* has the weak* Kadec-Klee property are characterised by a compactness...
On Weakly Compact Operators on C*-Algebras.
Open projections in operator algebras I: Comparison theory
We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rørdam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals...
Open projections in operator algebras II: Compact projections
We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of 'peak projections', and in the separable case compact projections are just the peak projections. We also establish new forms of the noncommutative Urysohn lemma relative to an operator algebra, and we show that a projection is compact iff the associated face in the state space of the algebra is...
Operator algebras
Operator entropy inequalities
We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting , and then give upper and lower bounds for as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004), 219-235] under...
Operator inequalities, geodesics and interpolation
Operator spaces and similarity problems.