泛函分析

We exhibit a new approach to the proofs of the existence of a large family of almost isometric ideals in nonseparable Banach spaces and existence of a large family of almost isometric local retracts in metric spaces. Our approach also…

We study spectral constants for convex domains $\Omega$ containing the spectrum of an operator. We extend the Crouzeix--Palencia framework by obtaining bounds depending on a parameter $\gamma$ and relating these bounds to geometric…

We introduce the mixed Bourgain-Morrey spaces and obtain their preduals. The boundedness of Hardy-Littlewood maximal operator, iterated maximal operator, fractional integral operator, singular integral operator on these spaces is proved. In…

The fine structures on the $S$-spectrum constitute a new research area that includes a class of functional calculi based on the $S$-spectrum and on integral transforms determined by the Fueter--Sce mapping theorem and the Cauchy formula for…

We study weighted residual dynamics associated with a rank-one projection in finite dimension. The iteration reduces, after finitely many steps, to a nonlinear recursion on a stabilized active subspace. We prove that this recursion can be…

We establish a reproducing formula for the ridgelet transform on $\mathbb{R}^n$ in the framework of Banach lattices introduced in a recent paper by Nieraeth. Our approach is based on the $k$-plane Radon transform and a wavelet-type…

We introduce a signature inversion scheme for $C^1$-axial linear curves which are widely used in various areas. We show that in the presence of a linear coordinate function, the derivatives of the underlying curve at any point $x$ can be…

We study Hardy--Sobolev spaces H_n^p(C^+) on the upper half-plane for 1<=p<=infty and n is a nonnegative integer, from both function-theoretic and operator-theoretic viewpoints. We establish an isometric boundary characterization of…

In this article, in order to the minimal operator generated by the first-order differential-operator expression in the weighted Hilbert space of vector functions in the finite interval to be formal normal, the relationship between the…

We characterize the boundedness of a positive integral operator $T_K$, with kernel $K\in M_+(\R^{2n})$, between Lorentz-Gamma spaces $\Gamma_{p,\phi_2}(\R^n)$ and $\Gamma_{q,\phi_1}(\R^n)$, $1<p\le q<\infty$. The key step reduces the…

We study whether essential positivity \[ \sigma_{\mathrm{ess}}(T_f)\subset [0,\infty) \] of a radial Toeplitz operator on Bergman and Fock spaces can be detected from the asymptotic behavior of its Berezin transform. For bounded real-valued…

Let $A$ be a Banach algebra and $I$ a dense ideal in $A$. A natural question in the theory of operator algebras is whether the property that all derivations $D: A \to I$ are inner (implemented by elements in $I$) implies that all…

We investigate the following general problem, closely related to the problem of isomorphic classification of Banach spaces $C(K)$ of continuous real-valued functions on a compact space $K$, equipped with the supremum norm: Let $\mathcal{K}$…

For a tuple $T$ of Hilbert space operators, the 'commuting dilation constant' is the smallest number $c$ such that the operators of $T$ are a simultaneous compression of commuting normal operators of norm at most $c$. We present numerical…

In this note, we demonstrate how determinant representations for correlation functions in conformal field theory can be used to derive explicit determinant formulas for powers of the classical $\eta$-function, expressed via deformed…

Let $M$ be a subset of $\mathbb{R}^n$. If $M$ is not porous, in particular if it has positive $n$-dimensional Lebesgue measure, we prove that the Lipschitz spaces $\mathrm{Lip}_0(M)$ and $\mathrm{Lip}_0(\mathbb{R}^n)$ are linearly…

We study the linear dynamics of the random sequence $(T_n(.))_{n \geq 1}$ of the operators $T_n(\omega) = T(\tau^{n-1}\omega) \dotsm T(\tau \omega) T(\omega), n \geq 1$. These products depend on an ergodic measure-preserving transformation…

We present a generalization of H\"older duality to algebra-valued pairings via $L^p$-modules. H\"older duality states that if $p \in (1, \infty)$ and $p^{\prime}$ are conjugate exponents, then the dual space of $L^p(\mu)$ is isometrically…

We prove that every element of a Lipschitz-free space admits an expression as a convex series of elements with compact support. As a consequence, we conclude that all extreme points of the unit ball of Lipschitz-free spaces are elementary…

We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore,…