Related papers: Matrix Algebras with a Certain Compression Propert…

We say that an algebra is zero-product balanced if $ab\otimes c$ and $a\otimes bc$ agree modulo tensors of elements with zero-product. This is closely related to but more general than the notion of a zero-product determined algebra of…

We show that a $C^*$-algebra $\mathfrak{A}$ which is stably isomorphic to a unital graph $C^*$-algebra, is isomorphic to a graph $C^*$-algebra if and only if it admits an approximate unit of projections. As a consequence, a hereditary…

Effect algebras were introduced as an abstract algebraic model for Hilbert space effects representing quantum mechanical measurements. We study additional structures on an effect algebra $E$ that enable us to define spectrality and spectral…

For a tuple $A=(A_0, A_1, ..., A_n)$ of elements in a unital Banach algebra ${\mathcal B}$, its {\em projective spectrum} $p(A)$ is defined to be the collection of $z=[z_0, z_1, ..., z_n]\in \pn$ such that $A(z)=z_0A_0+z_1A_1+... +z_nA_n$…

The relative commutant $A'\cap A^{\mathcal{U}}$ of a strongly self-absorbing algebra $A$ is indistinguishable from its ultrapower $A^{\mathcal{U}}$. This applies both to the case when $A$ is the hyperfinite II$_1$ factor and to the case…

It is shown that projectionless C*-algebras that tensorially absorb the Jiang-Su algebra have the property that every element is a limit of products of two nilpotents. This is then used to classify the approximate unitary equivalence…

Let $A$ be a unital $C^*$-algebra and let $U_0(A)$ be the group of unitaries of $A$ which are path connected to the identity. Denote by $CU(A)$ the closure of the commutator subgroup of $U_0(A).$ Let $i_A^{(1, n)}\colon…

Let $X$ be a compact metric space and let $\af$ be a homeomorphism on $X.$ Related to a theorem of Pimsner, we show that $C(X)\rtimes_{\af}\Z$ can be embedded into a unital simple AF-algebra if and only if there is a strictly positive…

We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…

In this work we characterise the C*-algebras A generated by projections with the property that every pair of projections in A has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this…

For every idempotent $Q$ on a Hilbert space $H$, the matched projection $m(Q)$ is a well-established concept. This paper explores several applications of the matched projections. The first application addresses the distances from…

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

Nuclear C*-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in…

For any unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal traces, we prove that Z-absorption, strict comparison, and property (SI) are equivalent. We also show that any unital separable simple…

We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…

This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable ${\cal Z}$-absorbing C*-algebras with locally finite decomposition property satisfying the UCT whose…

Let $\Lambda$ be an Auslander's 1-Gorenstein Artinian algebra with global dimension two. If $\Lambda$ admits a trivial maximal 1-orthogonal subcategory of $\mod\Lambda$, then for any indecomposable module $M \in \mod \Lambda$, we have that…

In this paper, we study the notion of a separability idempotent in the C*-algebra framework. This is analogous to the notion in the purely algebraic setting, typically considered in the case of (finite-dimensional) algebras with identity,…

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

Given a (reduced) locally compact quantum group $A$, we can consider the convolution algebra $L^1(A)$ (which can be identified as the predual of the von Neumann algebra form of $A$). It is conjectured that $L^1(A)$ is operator biprojective…