Related papers: Projection decomposition in multiplier algebras

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

Let $M$ be a type ${\rm II}$ factor and let $\tau$ be the faithful positive semifinite normal trace, unique up to scalar multiples in the type ${\rm II}_\infty$ case and normalized by $\tau(I)=1$ in the type ${\rm II}_1$ case. Given $A\in…

A module $M$ is {called} stable if it has no nonzero projective direct summand. For a ring $ R $, we study conditions under which $R$-modules from certain classes decompose as a direct sum of a projective submodule and a stable submodule.…

In this short note, we prove that for a $C^*$-algebra $\aa$ generated by $n$ elements, $M_{k}(\tilde{\aa})$ is generated by $k$ mutually unitarily equivalent and almost mutually orthogonal projections for any $k\ge…

An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be \textit{idempotent compressible} if $E\mathcal{A}E$ is an algebra for all idempotents $E\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be…

In this paper we prove that every set $A\subset\mathbb{Z}$ satisfying the inequality $\sum_{x}\min(1_A*1_A(x),t)\le(2+\delta)t|A|$ for $t$ and $\delta$ in suitable ranges, then $A$ must be very close to an arithmetic progression. We use…

The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We consider polynomials $p(a,a^*)$ for elements $a$ with small self-commutator norm $\|[a,a^*]\| \le \delta$ and show that many properties of…

We define the class of weakly approximately divisible unital C*-algebras and show that this class is closed under direct sums, direct limits, any tensor product with any C*-algebra, and quotients. A nuclear C*-algebra is weakly…

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…

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

We show that for a large class of C*-algebras $\mathcal{A}$, containing arbitrary direct limits of separable type I C*-algebras, the following statement holds: If $A\in \mathcal{A}$ and $B$ is a simple projectionless C*-algebra with trivial…

We study maps between positive definite or positive semidefinite cones of unital $C^*$-algebras. We describe surjective maps that preserve (1) the norm of the quotient or multiplication of elements; (2) the spectrum of the quotient or…

We classify all essential extensions of the form $$0 \rightarrow \W \rightarrow \D \rightarrow A \rightarrow 0$$ where $\W$ is the unique separable simple C*-algebra with a unique tracial state, with finite nuclear dimension and with…

We prove a reduction theorem for capacity of positive maps of finite dimensional C*-algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.

We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…

Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…

In a pure C*-algebra (i.e., one having suitable regularity properties in its Cuntz semigroup), any element on which all bounded traces vanish is a sum of 7 commutators.

We consider two twisted actions of a countable discrete group on $\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as…

We say that a unital C*-algrebra A has the approximate positive factorization property (APFP) if every element of A is a norm limit of products of positive elements of A. (There is also a definition for the nonunital case.) T. Quinn has…

H. Dye defined the projections $P_{i,j}(a)$ of a $C^*$-matrix algebra by {eqnarray*} P_{i,j}(a) &=& (1+aa^*)^{-1}\otimes E_{i,i} + (1+aa^*)^{-1}a \otimes E_{i,j} + a^*(1+aa^*)^{-1} \otimes E_{j,i} + a^*(1+aa^*)^{-1}a\otimes E_{j,j},…