We present several applications of the Assouad dimension, and related quasi-Assouad dimension spectrum, to box packing dimensions orthogonal projections sets. For example, we show that if (quasi-)Assouad $F \subseteq\mathbb{R}^n$ is no greater than $m$, then $F$ are preserved under onto almost all $m$-dimensional subspaces. also threshold $m$ for sharp, bound exceptional set strictly away from ...

In [4], the notion of a complete one-sided M -ideal for an operator space X was introduced as a generalization of Alfsen and Effros’ notion of an M -ideal for a Banach space [1]. In particular, various equivalent formulations of complete one-sided M -projections were given. In this paper, some sharper equivalent formulations are given in the special situation that X = A, a C∗-algebra (in which ...

Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies...

In this note we include two remarks about bounded (not necessarily contractive) linear projections on a von Neumann-algebra. We show that if M is a von Neumann-subalgebra of B(H) which is complemented in B(H) and isomorphic to M ⊗ M then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part,we show that ...

In [4], the notion of a complete one-sided M-ideal for an operator space X was introduced as a generalization of Alfsen and Effros' notion of an M-ideal for a Banach space [1]. In particular, various equivalent formulations of complete one-sided M-projections were given. In this paper, some sharper equivalent formulations are given in the special situation that X = A, a C *-algebra (in which ca...

Let X be a compact metric space which is locally absolutely retract and let ϕ: C(X) → C(Y,M(n)) be a unital homomorphism, where Y is a compact metric space with dim Y ≤ 2. It is proved that there exists a sequence of n continuous maps α(i,m): Y → X (i = 1,2,…,n) and a sequence of sets of mutually orthogonal rank-one projections {p(1,m),p(2,m),…,p(n,m)} C(Y,M(n)) such that [see formula]. This is...

In this paper, we introduce the notion of $$\mathbb {M}_2$$ -strict projections in $$M_2(\mathcal {M}_0)$$ where $$\mathcal {M}_0$$ is an abelian von Neumann algebra and prove that absolutely compatible pair strict elements a {M}$$ unitarily equivalent to $$\left( (1 - x_0) \otimes I_2 \right) P_0 + (x_0 I_2) P$$ P'$$ algebra, $$x_0$$ element {M}_0^+$$ , $$P_0 = \begin{bmatrix} 0 &{} \\ 1 \end{...

COMPOSITIONS OF SPECIES STEFAN FORCEY Abstract. An extension of the Tamari lattice to the multiplihedra is discussed, along with projections to the composihedra and the Boolean lattice. The multiplihedra and composihedra are sequences of polytopes that arose in algebraic topology and category theory. Here we describe them in terms of the composition of combinatorial species. We de ne lattice st...

Blind Source Separation consists of estimating n sources from the measurements provided by m sensors. In this paper we deal with the underdetermined case, m < n, where the solution can be implemented in two stages: first estimate the mixing matrix from the measurements and then estimate the best solution to the underdetermined linear problem. Instead of being restricted to the conventional two-...

Applying self-consistent field theory, we consider a coarse-grained model for the polymerlike projections of neurofilament (NF) proteins that form a brush structure around neurofilaments. We focus on effects of molecular composition, which is the relative occurrence of NF-H, NF-M, and NF-L proteins, on the organization of NF projection domains. We consider NF brushes with selectively truncated ...