Related papers: A note on the maximal numerical range
For any simple digraph $D$ we offer a new proof for the intersection number of its middle digraph, $M(D)$; while doing so we also solve for the intersection number when $D$ has loops. In addition, a new transformation, the union of $D$ and…
We associate to any given finite set of valuations on the polynomial ring in two variables over an algebraically closed field a numerical invariant whose positivity characterizes the case when the intersection of their valuation rings has…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
We investigate the generalized quadratic operator defined by $$T =\left( \begin{array}{cc} a I_H & A \\ c A^* & bI_K \end{array} \right) ,$$ where $H$ and $K$ are Hilbert spaces, $A:K\to H$ is a bounded linear operator, $I_H$ and $I_K$…
We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. Among many other inequalities proved in this article, we show that for a…
We define the complete numerical radius norm for homomorphisms from any operator algebra into ${\mathcal B}({\mathcal H})$, and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show…
Using some resolution of singularities and oscillatory integral methods in conjunction with appropriate damping and interpolation techniques, L^p boundedness theorems for p > 2 are obtained for maximal operators over a wide range of…
Matroid is a generalization of many fundamental objects in combinatorial mathematics , and matroid intersection problem is a classical subject in combinatorial optimization . However , only the intersection of two matroids are well…
Consider a complex Hilbert space $\left(\mathcal{H}, \langle \cdot, \cdot \rangle\right)$ equipped with a positive bounded linear operator $A$ on $\mathcal{H}$. This induces a semi-norm $\|\cdot\|_A$ through the semi-inner product $\langle…
We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.
We characterize, in the context of rearrangement invariant spaces, the optimal range space for a class of monotone operators related to the Hardy operator. The connection between optimal range and optimal domain for these operators is…
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
In this paper it is shown that a complete graph with $n$ vertices has an optimal diagram, i.e., a diagram whose crossing number equals the value of Guy's formula, with a free maximal linear tree and without free hamiltonian cycles for any…
This paper explores the fundamental properties of distributed minimization of a sum of functions with each function only known to one node, and a pre-specified level of node knowledge and computational capacity. We define the optimization…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
This article introduces several new upper bounds for the $q$-numerical radius of bounded linear operators on complex Hilbert spaces. Our results refine some of the existing upper bounds in this field. The $q$-numerical radius inequalities…
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that the numerical radius of A and of its inverse are no greater than 1+e for some non-negative e. It is shown that…
A drawing of a graph in the plane is a thrackle if every pair of edges intersects exactly once, either at a common vertex or at a proper crossing. Conway's conjecture states that a thrackle has at most as many edges as vertices. In this…
In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff-James orthogonality techniques, we give a necessary condition for a bounded linear operator…
We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a…