Related papers: A note on two-sided ideals in locally C*-algebras

It has been established by Inoue that a complex locally C*-algebra with a dense ideal posesses a bounded approximate identity which belonges to that ideal. It has been shown by Fritzsche that if a unital complex locally C*-algebra has an…

In this paper an automorphism of a unital C*-algebra is said to be /locally inner/ if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating…

A theorem is presented on existence and uniqueness up to the topological *-isomorphism of universal locally C*-algebra for an arbitrary locally JB-algebra.

We explicitly describe two-sided ideals in Leavitt path algebras associated with a row-finite graph. Our main result is that any two-sided ideal $I$ of a Leavitt path algebra associated with a row-finite graph is generated by elements of…

We show that a unital ring is generated by its commutators as an ideal if and only if there exists a natural number $N$ such that every element is a sum of $N$ products of pairs of commutators. We show that one can take $N \leq 2$ for…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…

This note proves that there exists positive constants $c_1$ and $c_2$ such that for all finite $A \subset \mathbb R$ with $|A+A| \leq |A|^{1+c_1}$ we have $|AAA| \gg |A|^{2+c_2}$.

Let $A,B$ be C*-algebras, $B_A(0;r)$ the open ball in $A$ centered at $0$ with radius $r>0$, and $H:B_A(0;r)\to B$ an orthogonally additive holomorphic map. If $H$ is zero product preserving on positive elements in $B_A(0;r)$, we show, in…

We introduce a generalization of the notion of local homology module, which we call a local homology module with respect to a pair of ideals $\left(I,J\right)$, and study its various properties such as vanishing, co-support and…

Order unit property of a positive element in a $C^{*}$-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary $C^{*}$-subalgebras of a $C^{*}$-algebra are…

In this article it is proved that for every special AJW-algebra $A$ there exist central projections $e$, $f$, $g\in A$, $e+f+g=1$ such that (1) $eA$ is reversible and there exists a norm-closed two sided ideal $I$ of $C^*(eA)$ such that…

Let C be a Cantor set. For a real number t let C+t be the translate of C by t, We say two real numbers s,t are equivalent if the intersection of C and C+s is a translate of the intersection of C and C+t. We consider a class of Cantor sets…

A left ideal of any C*-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Conversely, we show here and in a `pre-quel' to this paper [B], that operator algebras with r.c.a.i. should be…

The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative…

In this paper, we characterize $\ell$-open and $\ell$-closed $C^*$-algebras and deduce that $\ell$-open $C^*$-algebras are $\ell$-closed, as conjectured by Blackadar. Moreover, we show that a commutative unital $C^*$-algebra is $\ell$-open…

We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…

The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: the first one takes into account the inductive structure provided by certain families of…

Let $X$ be a locally compact non compact Hausdorff topological space. Consider the algebras $C(X)$, $C_b(X)$, $C_0(X)$, and $C_{00}(X)$ of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions…

Let $R$ be a commutative ring with unity. The prime ideal sum graph of the ring $R$ is a simple undirected graph whose vertex set is the set of nonzero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if…

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of…