泛函分析

We extend the important generalizations by Yannelis [25] and Cornet et al [7] of the classical result of Gale, Nikaido, Kuhn and Debreu (the "GNKD theorem") regarding existence of market equilibrium, by broadening the applicability of their…

We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.

We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.

We present estimates for the covering numbers of the unit ball of Reproducing Kernel Hilbert Spaces (RKHSs) of functions on $M^d$ a d-dimensional compact two-point homogeneous space. The RKHS is generated by a continuous zonal/isotropic…

In 1951 paper \cite{Ki} Kippenhahn conjectured that if the characteristic polynomial \ $P_A(x_1,x_2,x_3)=\mbox{det}(x_1A_1+x_2A_2-x_3I)$, \ where $A_1$ and $A_2$ are $n\times n$ Hermitian matrices, has a repeated factor in the polynomial…

In a companion paper (Studia Math., 2023), we proved for every $\lambda\in(1,2]$ the existence of a $(\lambda^+)$-injective renorming of $\ell_\infty$ that is not $\lambda$-injective, thereby establishing a~forgotten theorem of…

In this paper, our main goal is to define the class of weakly Demi Dunford-Pettis applications. We also study their relationship with the classes of weakly Dunford-Pettis and Demi Dunford-Pettis operators, including a condition where these…

Building on a recent construction of Plebanek and Salguero-Alarc\'on, which solved the Complemented Subspace Problem for $C(K)$-spaces, and the subsequent work of De Hevia, Mart\'inez-Cervantes, Salguero-Alarc\'on, and Tradacete solving the…

Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of…

We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and…

We prove Banach, Newton-Raphson and Brouwer fixed point theorems in the framework of generalized smooth functions, a minimal extension of Colombeau's theory (and hence of classical distribution theory) which makes it possible to model…

We characterize the spectrum of Hausdorff operators on weighted Bergman and power weighted Hardy spaces of the upper half-plane.

We establish a new pointwise estimate for a class of rough operators in the setting of metric measure spaces endowed with a measure which is Ahlfors regular. This pointwise inequality can be divided in two steps: the first one relies in a…

Let $B(\mathcal{H})$ denote the $C^*$-algebra of all bounded linear operators acting on a reproducing kernel Hilbert space $\mathcal{H}(\Omega).$ In this paper, we introduce a new family of seminorms on $B(\mathcal{H})$, called the…

Within the framework of quantum harmonic analysis, for a locally compact group $G$ with a square-integrable, irreducible unitary representation, we analyze the eigenvalue distributions of convolutions between indicator functions on $G$ and…

In this paper, we investigate $\mathbb T^d$-invariant Hilbert modules $\mathscr H$ over the polynomial ring $\mathbb C[z_1, \ldots, z_d]$ and their quotients, with primary emphasis on the classification of subnormal quotient modules of the…

The aim of this paper is to study the problem of the integration of Stepanov remotely almost periodic functions. We prove that every compact primitive of a Stepanov remotely almost periodic function with a minimal $\omega$-limit set is…

This article was initially motivated by our goal to show that the Banach space $\mathbb{G}$ constructed by Gowers in [W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), no. 6, 523-530] to settle…

In this paper, a universal approximation theorem (UAT) for shallow neural networks whose inputs belong to a topological vector space (TVS) and whose outputs take values in a Hausdorff locally convex TVS is established. The networks are…

This paper addresses the extension of the Stockwell transform to Gelfand pairs. Some majors properties of this transform are examined. The localization operators related to the Stockwell transform in this framework are studied.