ﻻ يوجد ملخص باللغة العربية
Let $mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(mathcal{M},tau)$, with $0<p<infty$, into each topological linear space $X$ with the property that $P(x+y)=P(x)+P(y)$ whenever $x$ and $y$ are mutually orthogonal positive elements of $L^p(mathcal{M},tau)$ can be represented in the form $P(x)=Phi(x^m)$ $(xin L^p(mathcal{M},tau))$ for some continuous linear map $Phicolon L^{p/m}(mathcal{M},tau)to X$.
Let $mathcal{M}$ be a von Neumann algebra, and let $0<p,qleinfty$. Then the space $Hom_mathcal{M}(L^p(mathcal{M}),L^q(mathcal{M}))$ of all right $mathcal{M}$-module homomorphisms from $L^p(mathcal{M})$ to $L^q(mathcal{M})$ is a reflexive subspace of
Based on the characterization of surjective $L^p$-isometries of unitary groups in finite factors, we describe all surjective $L^p$-isometries between Grassmann spaces of projections with the same trace value in semifinite factors.
Let $X$ and $Y$ be Banach spaces, let $mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $Pcolonmathcal{A}(X)to Y$ be an orthogonally additive, continuous $n$-homogeneous polynomial. If $X^*$ has the bounded approximatio
We apply Arvesons non-commutative boundary theory to dilate every Toeplitz-Cuntz-Krieger family of a directed graph $G$ to a full Cuntz-Krieger family for $G$. We do this by describing all representations of the Toeplitz algebra $mathcal{T}(G)$ that
Let $G$ be a compact group, let $X$ be a Banach space, and let $Pcolon L^1(G)to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $Phicolon L^1(G)to X$ such that $P(f)