Related papers: Convolution operators preserving the set of totall…

Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem} asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9…

In this paper, our primary objective is to study a possible decomposition of an approximately convex sequence. For a given $\varepsilon>0$; a sequence $\big<u_n\big>_{n=0}^{\infty}$ is said to be $\varepsilon$-convex, if for any…

Inspired by the classical Bohman-Korovkin-Wulbert (BKW) operators, we initiate a study of noncommutative BKW-operators. Let $A$ be a unital $C^*$-algebra, and $S$ be a set of generators of $A$. A unital completely positive (UCP)-map $\phi:…

Let $v_1$,..., $v_n$ be $n$ vectors in an inner product space. Can we find a natural number $d$ and positive (semidefinite) complex matrices $A_1$,..., $A_n$ of size $d \times d$ such that ${\rm Tr}(A_kA_l)= <v_k, v_l>$ for all $k,l=1,...,…

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…

A nondecreasing sequence of positive integers is $(\alpha,\beta)$-Conolly, or Conolly-like for short, if for every positive integer $m$ the number of times that $m$ occurs in the sequence is $\alpha + \beta r_m$, where $r_m$ is $1$ plus the…

Let $\ell^p$ be the space of all $p$-summable sequences on $\mathbb{Z}$. An infinite matrix is said to have $\ell^p$-stability if it is bounded and has bounded inverse on $\ell^p$. In this paper, a practical criterion is established for the…

Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining…

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every…

In this paper, we give conditions forcing nilpotent matrices (and bounded linear operators in general) to be null or equivalently to be normal. Therefore, a non-zero operator having e.g. a positive real part is never nilpotent. The case of…

In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and based on the notion of signatures of hermitian forms [1]. In…

In this paper we show that for a non-negative operator monotone function $f$ on $[0, \infty)$ such that $f(0)= 0$ and for any positive semidefinite matrices $A$ and $B$, $$ Tr((A-B)(f(A)-f(B))) \le Tr(|A-B|f(|A-B|)). $$ When the function…

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube…

In this paper, we investigate the well-posedness and positivity property of infinite-dimensional linear system with unbounded input and output operators. In particular, we characterize the internal and external positivity for this class of…

We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as…

It is proven that the absolutely continuous spectrum of matrix Schr\"{o}dinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The…

Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse…

Given an irreducible representation of a group G, we show that all the covariant positive operator valued measures based on G/Z, where Z is a central subgroup, are described by trace class, trace one positive operators.

We examine the fixed space of positive trace-preserving super-operators. We describe a specific structure that this space must have and what the projection onto it must look like. We show how these results, in turn, lead to an alternative…

For any irrational $\alpha > 0$ and any initial value $z_{-1} \in \mathbb{C}$, we define a sequence of complex numbers $(z_n)_{n=0}^{\infty}$ as follows: $z_n$ is $z_{n-1} + e^{2 \pi i \alpha n}$ or $z_{n-1} - e^{2 \pi i \alpha n}$,…