Related papers: Two projections in a synaptic algebra
According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex…
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…
The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…
Let $\mathcal S$ be a semigroup of partial isometries acting on a complex, infinite-dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup $\mathcal T$ generated by $\mathcal…
In this paper we prove that given any two point lattices $\Lambda_1 \subset \mathbb{R}^n$ and $ \Lambda_2 \subset \nobreak \mathbb{R}^{n-k}$, there is a set of $k$ vectors $\bm{v}_i \in \Lambda_1$ such that $\Lambda_2$ is, up to similarity,…
We study the well-known methods of alternating and simultaneous projections when applied to two nonorthogonal linear subspaces of a real Euclidean space. Assuming that both of the methods have a common starting point chosen from either one…
In this paper, we introduce the concept of trace-open projections in the second dual A** of a C*-algebra A, and we show that if there is a faithful normal semi-finite trace T on A**, and 1 is a T-open projection, then each 2-local…
We define a semi-Hopf algebra which is more general than a Hopf algebra. Then we construct the supersymmetry algebra via the adjoint action on this semi-Hopf algebra. As a result we have a supersymmetry theory with quantum gauge group,…
This paper has been withdrawn by the author, since the main result, the existence and uniqueness theorem for host algebras, Theorem 3.4, is wrong for the following reasons. In Definition 3.1 we wanted to generalise the concept of an open…
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…
In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be…
Let $A$ be a closed affine subspace and let $B$ be a hyperplane in a Hilbert space. Suppose we are given their associated nearest point mappings $P_A$ and $P_B$, respectively. We present a formula for the projection onto their intersection…
We study the orthogonal projections of symplectic balls in $\mathbb{R}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this theme by studying two interconnected problems regarding…
We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e.,…
We study operators that are products of two orthogonal projections. Our results complement some of the classical results of Crimmins and von Neumann. Particular emphasis has been given to projections associated with inner functions defined…
We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…
In 1933 von Neumann proved a beautiful result that one can approximate a point in the intersection of two convex sets by alternating projections, i.e., successively projecting on one set and then the other. This algorithm assumes that one…
If $V$ is a vector space over a field $F$, then we consider the projection from the tensor algebra to the symmetric algebra, $\rho_{T,S}:T(V)\to S(V)$. Our main result, in $\S$1, gives a description of $\ker\rho_{T,S}$. Explicitly, we…