Related papers: Duality for unbounded order convergence and applic…
The numerical index of a Banach space is a geometric constant relating the numerical radius of bounded linear operators to their standard operator norm. In this paper, we study the continuity of the numerical index under two distinct…
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…
The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…
It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal…
We establish the Subgradient Theorem for monotone correspondences -- a monotone correspondence is equal to the subdifferential of a potential if and only if it is conservative, i.e. its integral along a closed path vanishes irrespective of…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
In this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we…
We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is…
We provide a new extension of Pitt's theorem for compact operators between quasi-Banach lattices, which permits to describe unconditional bases of finite direct sums of Banach spaces $\mathbb{X}_{1}\oplus\dots\oplus\mathbb{X}_{n}$ as direct…
For every filter $\mathcal F$ on $\mathbb N$, we introduce and study corresponding uniform $\mathcal F$-boundedness principles for locally convex topological vector spaces. These principles generalise the classical uniform boundedness…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
Let $(x_\alpha)$ be a net in a vector lattice normed by locally solid lattice $(X,p,E_\tau)$. We say that $(x_\alpha)$ is unbounded $p_\tau$-convergent to $x\in X$ if $p(\lvert x_\alpha-x\rvert\wedge u)\xrightarrow{\tau} 0$ for every $u\in…
Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice DC rather than the…
We prove when a Banach ideal of linear operators defined, or characterized, by the transformation of vector-valued sequences is maximal. Known results are recovered as particular cases and new information is obtained. To accomplish this…
The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension…
In this paper we consider a dual gradient method for solving linear ill-posed problems $Ax = y$, where $A : X \to Y$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y$. A strongly convex penalty function is used in…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…
Having been unclear how to define that a domain is strictly pseudoconvex in the infinite-dimensional setting, we develop a general theory having Banach spaces in mind. We first focus on finite dimension and eliminate the need of two degrees…