Related papers: Operator Lipschitz Functions

Let $\Lambda_s$ denote the Lipschitz space of order $s\in(0,\infty)$ on $\mathbb{R}^n$, which consists of all $f\in\mathfrak{C}\cap L^\infty$ such that, for some constant $L\in(0,\infty)$ and some integer $r\in(s,\infty)$, \begin{equation*}…

On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions.…

The main result of this paper is a description of the space of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. This space coincides with the space of…

To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…

An additive map $T$ acting between spaces of vector-valued functions is said to be biseparating if $T$ is a bijection so that $f$ and $g$ are disjoint if and only if $Tf$ and $Tg$ are disjoint. Note that an additive bijection retains…

Let $B_E$ be the open unit ball of a complex finite or infinite dimensional Hilbert space. If $f$ belongs to the space $\mathcal{B}(B_E)$ of Bloch functions on $B_E$, we prove that the dilation map given by $x \mapsto (1-\|x\|^2)…

We study an elliptic differential operator A on a manifold with conic points. Assuming A to be defined on the smooth functions supported away from the singularities, we first address the question of possible closed extensions of A to L^p…

Consider a Henselian rank one valued field $K$ of equicharacteristic zero with the three-sorted language $\mathcal{L}$ of Denef--Pas. Let $f: A \to K$ be a continuous $\mathcal{L}$-definable (with parameters) function on a closed bounded…

We give some new characterizations of strictly Lipschitz p-summing operators. These operators have been introduced in order to improve the Lipschitz p-summing operators. Therefore, we adapt this definition for constructing other classes of…

The main result of the paper is a description of the class of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. We prove that this class of functions…

Let $X$ be a separable Banach space with a separating polynomial. We show that there exists $C\geq 1$ (depending only on $X$) such that for every Lipschitz function $f:X\rightarrow\mathbb{R}$, and every $\epsilon>0$, there exists a…

Let (X,d) be a metric space and $ \alpha > 0 $. In this paper, we study extensions of some complex-valued Lipschitz functions, from some special subset $ X_0 $ to X. These extensions are with no-increasing Lipschitz number or the smallest…

We consider weighted composition operators, that is operators of the type $g \mapsto w \cdot g \circ f$, acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition…

We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer G-functions of |x|^2, or generalized…

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators $\{ T_m: \, m \ge 1\}$ given by $T_m(f)(a, c) = \frac{1}{m} \sum_{k=0}^{m-1} f(\frac{a+k}{m},…

In this work, we study the composition operators on the little Lipschitz space ${\mathcal L}_0$ of a rooted tree $T$, defined as the subspace of the Lipschitz space ${\mathcal L}$ consisting of the complex-valued functions $f$ on $T$ such…

The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix…

Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is…

In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this…

The variance of a bounded linear operator $a$ on a Hilbert space $H$ at a unit vector $h$ is defined by $D_h(a)=\|ah\|^2-|<ah,h>|^2$. We show that two operators $a$ and $b$ have the same variance at all vectors $h\in H$ if and only if there…