Related papers: Separably injective C*-algebras

We continue our investigation, from \cite{dh}, of the ring-theoretic infiniteness properties of ultrapowers of Banach algebras, studying in this paper the notion of being purely infinite. It is well known that a $C^*$-algebra is purely…

In a previous paper the second author introduced a compact topology on the space of closed ideals of a unital Banach algebra A. If A is separable then this topology is either metrizable or else neither Hausdorff nor first countable. Here it…

We characterise the positive cone of a real C*-algebra geometrically. Given an open cone $\Omega$ in a real Banach space $V$, with closure $\overline \Omega$, we show that $\Omega$ is the interior of the positive cone of a unital real…

We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)),…

It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$ and $K_B$…

Let CBV denote the Banach algebra of all continuous real-valued functions of bounded variation, defined in [0,1]. We show that the set of strongly singular functions in CBV is nonseparably spaceable. We also prove that certain families of…

We prove that any separable exact C*-algebra is isomorphic to a subalgebra of the Cuntz algebra ${\cal O}_2.$ We further prove that if $A$ is a simple separable unital nuclear C*-algebra, then ${\cal O}_2 \otimes A \cong {\cal O}_2,$ and…

A Banach involutive algebra is called a Krein C*-algebra if there is a fundamental symmetry (an involutive automorphism of period 2) such that the C*-property is satisfied when the original involution is replaced with the new one obtained…

We analyze certain algebraic structures of the Banach space projective tensor product of $C^*$-algebras which are comparable with their known counterparts or the Haagerup tensor product and the operator space projective tensor product of…

The classical Banach--Mazur theorem asserts that every separable Banach space admits an isometric embedding into $C[0,1]$. It is also well known that every separable Banach space embeds isometrically into $\ell^\infty$. We show that such an…

The local multiplier C*-algebra M_{loc}(A) of any C*-algebra A can *-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is…

We propose a unified approach to the study of isometries on algebras of vector-valued Lipschitz maps and those of continuously differentiable maps by means of the notion of admissible quadruples. We describe isometries on function spaces of…

We show the existence of a compact metric space $K$ such that whenever $K$ embeds isometrically into a Banach space $Y$, then any separable Banach space is linearly isometric to a subspace of $Y$. We also address the following related…

We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify projective $C^*$-algebras $\A$ defined by locally…

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$…

Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on…

Following a result of Hatori, Miura and Tagaki ([4]) we give here a spectral characterization of an isomorphism from a $C^\star$-algebra onto a Banach algebra. We then use this result to show that a $C^\star$-algebra $A$ is isomorphic to a…

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…