泛函分析
Reproducing kernel Hilbert spaces are uniquely characterized by their kernel, but reproducing kernel Banach spaces (RKBS) are not. However, a characterization of which RKBS admit a given kernel as reproducing kernel is lacking. This work…
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…
A classical result in approximation theory states that for any continuous function \( \varphi: \mathbb{R} \to \mathbb{R} \), the set \( \operatorname{span}\{\varphi \circ g : g \in \operatorname{Aff}(\mathbb{R})\} \) is dense in \(…
We characterize the strictly increasing symbols $\varphi:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_{\varphi}$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space…
We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions $c$, including Bregman and entropic transport divergences. We establish several properties of…
Given an open subset $U$ of a complex Banach space $E$, a weight $v$ on $U$, and a complex Banach space $F$, let $\Hv(U,F)$ denote the Banach space of all weighted holomorphic mappings $f\colon U\to F$, under the weighted supremum norm…
We characterize the matrices $U=(u_{ij})$ for which the operator square-sum identity $$\sum_{i=1}^m\Big|\sum_{j=1}^n u_{ij}A_j\Big|^2=\sum_{j=1}^n|A_j|^2$$ holds for all Schatten-class operators $A_1,\ldots,A_n$; this happens exactly when…
Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^m, \{\omega_k\}_{k=1}^m)$ be p-Schauder frames for a finite dimensional Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align}…
In 1963 Gr\"unbaum introduced the following variation of the Banach-Mazur distance for arbitrary convex bodies $K, L \subset \mathbb{R}^n$: $d_G(K, L) = \inf \{ |r| \ : \ K' \subset L' \subset rK' \}$ with the infimum taken over all…
The isometric dilation of a pair of commuting contractions due to And\^{o} is not minimal. We modify And\^{o}'s dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2 \ell_2(\mathcal H \oplus_2 \mathcal H)$ for a…
The structured singular value $\mu_E$ for a linear subspace $E$ of $M_n(\mathbb C)$ is defined by \[ \mu_E(A)=1 / \inf\{\|X\| \ : \ X \in E, \ \det(I_n-AX)=0 \} \quad (A \in M_n(\mathbb{C})), \] and $\mu_E(A)=0$ if there is no $X \in E$…
For an N-extremal solution $\mu$ to an indeterminate moment problem it is known by a theorem of M. Riesz that the measure $(1+x^2)^{-1}d\mu(x)$ is determinate. For $0<\alpha<1$ we show by contradiction that there exist indeterminate…
We establish a pointwise limit theorem for a broad class of pa\-ra\-me\-ter-\-de\-pen\-dent BMO-type seminorms as the parameter tends to zero. By introducing novel BMO-type seminorms, we provide a unified framework that extends several…
In this paper, we discuss three short topics related to the parity operator and his role in quantum harmonic analysis. We derive results for the Fredholm index of even and odd operators, discuss operators on which the modulation action acts…
We establish new optimal reversed Hardy-type inequalities on the cone of decreasing sequences from $\ell^p$-spaces with power weights, as well as estimates between different norms in Lorentz spaces of sequences. Based on these inequalities,…
We study spaces of essentially bounded functions on compact subsets of the real line, equipped with the Alexiewicz norm given by the supremum norm of the primitive. Using the associated measure projection, we classify their surjective…
We study the representation of non-weakly compact operators between $AL$-spaces. In this setting, we show that every operator admits a best approximant in the ideal of weakly compact operators. Using duality arguments, we extend this result…
The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of $C(X)$, the space of all continuous functions on a compact Hausdorff space is a classical problem that…
We study linear operators on a finite-dimensional space whose Kippenhahn curves consist of concentric circles centered at the origin. We say that such operators have Circularity property. One class of examples is rotationally invariant…
Recently the authors solved a long-standing problem and showed that for an arbitrary pair of contractions on Hilbert space with trace class difference has an integrable spectral shift function on the unit circle ${\Bbb T}$ and an analogue…