A weak vector-valued Banach–Stone theorem for Choquet simplices

2021 ◽  
Author(s):  
Jakub Rondoš ◽  
Jiří Spurný
Keyword(s):  
Vector Valued ◽  
Stone Theorem ◽  
Weak Vector

scholarly journals A weak vector-valued Banach-Stone theorem

2013 ◽  
Vol 141 (10) ◽  
pp. 3529-3538 ◽  
Author(s):  
Leandro Candido ◽  
Elói Medina Galego
Keyword(s):  
Vector Valued ◽  
Stone Theorem ◽  
Weak Vector

scholarly journals On V-r-invexity and vector variational-like inequalities

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 1065-1073 ◽  
Author(s):  
S.K. Mishra ◽  
Vivek Laha
Keyword(s):  
Multiobjective Optimization ◽  
Vector Optimization ◽  
Critical Points ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Multiobjective Optimization Problems ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Weak Vector

In this paper, we consider the multiobjective optimization problems involving the differentiable V-r-invex vector valued functions. Under the assumption of V-r-invexity, we use the Stampacchia type vector variational-like inequalities as tool to solve the vector optimization problems. We establish equivalence among the vector critical points, the weak efficient solutions and the solutions of the Stampacchia type weak vector variational-like inequality problems using Gordan?s separation theorem under the V-r-invexity assumptions. These conditions are more general than those appearing in the literature.

A vector-valued Banach–Stone theorem with distortion

2017 ◽  
Vol 290 (2) ◽  
pp. 321-332 ◽  
Author(s):  
Elói Galego ◽  
André Luis da Silva
Keyword(s):  
Vector Valued ◽  
Stone Theorem

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Generic rotation sets

2020 ◽  
pp. 1-13
Author(s):  
SEBASTIÁN PAVEZ-MOLINA
Keyword(s):  
Dynamical System ◽  
Convex Body ◽  
Probability Measures ◽  
Topological Dynamical System ◽  
Continuous Vector ◽  
Rotation Set ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Uniquely Ergodic ◽  
Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

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