The elements of bounded trace in the C*-algebra of a nilpotent Lie group.
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of -algebras
The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in -algebras. Since -algebras are natural generalizations of -algebras, -algebras, -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.
The Exponential Rank of Inductive Limit C*-Algebras.
The Facial Q-Topology for Compact Convex Sets.
The free cover of a row contraction.
The Frölicher-Nijenhuis bracket in non-commutative differential geometry.
The General Stone-Weierstrass Problem and Extremal Completely Positive Maps.
The graph traces of finite graphs and applications to tracial states of -algebras.
The group of automorphisms of is algebraically reflexive
We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of is [algebraically] reflexive if and only if is *-isomorphic to . For purely atomic measures, we show that the group of automorphisms (or isometries) of is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism group...
The group of invertible elements in a Banach algebra
The Group Property of the Invariant S of von Neumann Algebras.
The Herz-Schur multiplier norm of sets satisfying the Leinert condition
It is well known that in a free group , one has , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for .
The Hilbert projective metric and an equation in a -algebra
The ideal structure of the Haagerup tensor product of C*-algebras.
The index of projective families of elliptic operators.
The injective hull of an archimedean f-algebra
The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions.
The invertible elements are dense in the irrational rotation C*-algebras.
The isolated ideal of a correspondence associated with a topological quiver.
The joint approximate spectrum of a finite system of elements of a C*-algebra