Strong Klee–Andô Theorems through an Open Mapping Theorem for cone-valued multi-functions

Autor: Miek Messerschmidt

Publikováno v: Journal of Functional Analysis. 275:3325-3337

A version of the classical Klee-And\^o Theorem states the following: For every Banach space $X$, ordered by a closed generating cone $C\subseteq X$, there exists some $\alpha>0$ so that, for every $x\in X$, there exist $x^{\pm}\in C$ so that $x=x^{+}

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::009fcbfa1f6cc4aa9c6ba79c7908ae19
https://doi.org/10.1016/j.jfa.2018.02.008

Equivalence after extension and Schur coupling coincide for inessential operators

Autor: Mark Roelands, Miek Messerschmidt, Marten Wortel, André C. M. Ran, S. ter Horst

Publikováno v: ter Horst, S, Messerschmidt, M, Ran, A C M, Roelands, M & Wortel, M 2018, ' Equivalence after extension and Schur coupling coincide for inessential operators ', Indagationes Mathematicae, vol. 29, no. 5, pp. 1350-1361 . https://doi.org/10.1016/j.indag.2018.07.001
Indagationes Mathematicae, 29(5), 1350-1361. Elsevier

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::858b21122bbe0037057634d36008941e
https://hdl.handle.net/1871.1/0e907c43-f09d-4e88-ac6a-fcf92de8b7a8

A Pointwise Lipschitz Selection Theorem

Autor: Miek Messerschmidt

Publikováno v: Set-Valued and Variational Analysis. 27:223-240

We prove that any correspondence (multi-function) mapping a metric space into a Banach space that satisfies a certain pointwise Lipschitz condition, always has a continuous selection that is pointwise Lipschitz on a dense set of its domain. We apply

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ff29701417a9f32cdf125066ccbaba2e
https://doi.org/10.1007/s11228-017-0455-2

Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces

Autor: Miek Messerschmidt, Sanne ter Horst, André C. M. Ran, Mark Roelands

Publikováno v: Horst, S T, Messerschmidt, M, Ran, A C M & Roelands, M 2019, ' Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces ', Bulletin of the London Mathematical Society, vol. 51, no. 6, pp. 1005-1014 . https://doi.org/10.1112/blms.12292
Bulletin of the London Mathematical Society, 51(6), 1005-1014. Oxford University Press

In 1994 H. Bart and V.\'{E}. Tsekanovskii posed the question whether the Banach space operator relations matricial coupling (MC), equivalence after extension (EAE) and Schur coupling (SC) coincide, leaving only the implication EAE/MC $\Rightarrow$ SC

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c982831d8c1b214bc5b4bcf38c3b849
https://hdl.handle.net/10394/33600

Equivalence after extension for compact operators on Banach spaces

Autor: S. ter Horst, André C. M. Ran, Miek Messerschmidt

Publikováno v: Journal of Mathematical Analysis and Applications, 431(1), 136-149. Academic Press Inc.
van der Horst, S, Messerschmidt, M & Ran, A C M 2015, ' Equivalence after extension for compact operators on Banach spaces ', Journal of Mathematical Analysis and Applications, vol. 431, no. 1, pp. 136-149 . https://doi.org/10.1016/j.jmaa.2015.05.059

In recent years the coincidence of the operator relations equivalence after extension and Schur coupling was settled for the Hilbert space case, by showing that equivalence after extension implies equivalence after one-sided extension. In the present

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::351f0d421e6a93fb1607e305823f14eb
http://arxiv.org/abs/1503.07350