Related papers: Total Dilations

Let $F$ be an ordered topological vector space (over $\mathbb{R}$) whose positive cone $F_+$ is weakly closed, and let $E \subseteq F$ be a subspace. We prove that the set of positive continuous linear functionals on $E$ that can be…

Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H -> H. Identifying l^\infty = C(\beta N) with the diagonal operators, we consider…

We show that whenever a contractive $k$-tuple $T$ on a finite dimensional space $H$ has a unitary dilation, then for any fixed degree $N$ there is a unitary $k$-tuple $U$ on a finite dimensional space so that $q(T) = P_H q(U) |_H$ for all…

We offer a simple direct proof of the unitarity of the Julia operator associated to a contraction $A$, from which follow the intertwining identity $(I - A A^*)^{1/2} A = A (I - A^* A)^{1/2}$ and the unitarity of Halmos dilations.

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass…

We study the existence and characterization properties of compact Hermitian operators C on a separable Hilbert space H such that ||C|| is less or equal than || C + D ||, for all D in D(K(H)). This property is equivalent to || C || =…

Given a $\mathcal{C}^\infty$ expanding map $T$ of the circle, we construct a Hilbert space $\mathcal{H}$ of smooth functions on which the transfer operator $\mathcal{L}$ associated to $T$ acts as a compact operator. This result is made…

This article is to give an infinite dimensional analogue of a result of Choi and Effros. We say that an (not necessarily unital) operator system $T$ is \emph{dualizable} if one can find an equivalent dual matrix norm on the dual space $T^*$…

Let $T$ be a quadratic operator on a complex Hilbert space $H$. We show that $T$ can be written as a product of two positive contractions if and only if $T$ is of the form $$aI \oplus bI \oplus\begin{pmatrix} aI & P \cr 0 & bI \cr…

A bounded linear operator $A$ on a Hilbert space is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. Posinormality of $A$ is equivalent to the inclusion of the range of $A$ in the range of its adjoint $A^*$.…

Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…

Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…

Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, we explore a pure algebraic…

Let $U$ be an operator in a Hilbert space $\mathcal{H}_{0}$, and let $\mathcal{K}\subset\mathcal{H}_{0}$ be a closed and invariant subspace. Suppose there is a period-2 unitary operator $J$ in $\mathcal{H}_{0}$ such that $JUJ=U^*$, and $PJP…

In the article, we find new dilatation results on non-commutative $L_p$ spaces. We prove that any selfadjoint, unital, positive measurable Schur multiplier on some $B(L^2(\Sigma))$ admits, for all $1\leq p<\infty$, an invertible isometric…

Given commuting families of Hermitian matrices {A1, ..., Ak} and {B1, ...., Bk}, conditions for the existence of a completely positive map L, such that L(Aj) = Bj for j = 1, ...,k, are studied. Additional properties such as unital or / and…

It is proved that given $-1/2<s<1/2$, for any $f\in L^2(\mathbb{R})$, there is a unique $u\in \widehat{H}^{|s|}(\mathbb{R})$ such that $$ f=\boldsymbol{D}^{-s}u+\boldsymbol{D}^{s*}u\,, $$ where $\boldsymbol{D}^{-s}, \boldsymbol{D}^{s*}$ are…