Related papers: Intersecting Jones projections

The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…

In this note we include two remarks about bounded ($\underline{not}$ 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…

We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional…

We consider a Hilbert space ${\bf H}$ equipped with a set of strongly continuous bounded semigroups satisfying certain conditions. The conditions allow to define a family of moduli of continuity $\Omega^{r}(s,f),\>r\in \mathbb{N}, s>0,$ of…

A few years ago, Richard Kadison thoroughly analysed the diagonals of projection operators on Hilbert spaces and asked the following question: Let $\mathcal{A}$ be a masa in a type $II_1$ factor $\mathcal{M}$ and let $A \in \mathcal{A}$ be…

We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we…

In this paper we provide a quantitative comparison of two obstructions for a given symmetric operator S with dense domain in Hilbert space ${\cal H}$ to be selfadjoint. The first one is the pair of deficiency spaces of von Neumann, and the…

If there exists a completely bounded projection of B(H) onto a von Neumann algebra M on H, then M is injective. If there exists a bounded projection and M is properly infinite, the same conclusion holds.

Let $A$ be a unital $C^*$-algebra containing a closed two-sided ideal $J$ and an operator system $X$. We enlarge $X$ to an operator system $\mathcal{S}(X,J)$ in $\mathbb{M}_2(A)$, and show that in order for $\mathcal{S}(X,J)$ to be…

Based on the analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Mar\'echal topology on the space vN(H) of von Neumann algebras acting on a separable Hilbert space H, we show that for a von Neumann algebra M in vN(H), the…

The geometry conjecture, which was posed nearly a quarter of a century ago, states that the fixed point set of the composition of projectors onto nonempty closed convex sets in Hilbert space is actually equal to the intersection of certain…

Let M be a von Neumann algebra of type II_1 which is also a complemented subspace of B(H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented…

Given a class of functions $F$ on a probability space $(\Omega,\mu)$, we study the structure of a typical coordinate projection of the class, defined by $\{(f(X_i))_{i=1}^N : f \in F\}$, where $X_1,...,X_N$ are independent, selected…

Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ We describe class of von Neumann algebras $M$ for which the algebra $E(M)$ coincides with the algebra $S(M)$ -- the algebra of all measurable operators with…

We give an affirmative answer to the question whether there exist Lie algebras for suitable closed subgroups of the unitary group $U(\mathcal{H})$ in a Hilbert space $\mathcal{H}$ with $U(\mathcal{H})$ equipped with the strong operator…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

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…

We investigate surjective isometries between projection lattices of two von Neumann algebras. We show that such a mapping is characterized by means of Jordan $^*$-isomorphisms. In particular, we prove that two von Neumann algebras without…

This paper is mainly devoted to the following question:\ Let $M,N$ be von~Neumann algebras with $M\subset N$, if there is a completely bounded projection $P\colon \ N\to M$, is there automatically a contractive projection $\widetilde…

We present an extension of Naimark's duality principle which states that complete systems in a Hilbert space are projections of $\omega$-linearly independent systems of elements of an ambient Hilbert space. This result is presented in the…