ﻻ يوجد ملخص باللغة العربية
We study refinements between spectral resolutions in an arbitrary II$_1$ factor $M$ and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an application we obtain new characterizations of sub-majorization and spectral preorder between positive operators in $M$ and n
Suppose that $phi$ and $psi$ are smooth complex-valued functions on the circle that are invertible, have winding number zero with respect to the origin, and have meromorphic extensions to an open neighborhood of the closed unit disk. Let $T_phi$ and
In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:ell ^{2}(mathbb{N}) to H$, the analysis operator $T^{ast}:Hto $ $% ell ^{2}(mathbb{N}) $ and the associated frame operat
In this paper, we study the reducing subspaces for the multiplication operator by a finite Blaschke product $phi$ on the Dirichlet space $D$. We prove that any two distinct nontrivial minimal reducing subspaces of $M_phi$ are orthogonal. When the ord
Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $Gtimes Y$, such that $H$ is naturally embedded into $L^2(Gtimes Y)$ and is invariant u
Let $A = (a_{j,k})_{j,k=-infty}^infty$ be a bounded linear operator on $l^2(mathbb{Z})$ whose diagonals $D_n(A) = (a_{j,j-n})_{j=-infty}^inftyin l^infty(mathbb{Z})$ are almost periodic sequences. For certain classes of such operators and under certai