Normal Functionals on Lipschitz Spaces are Weak* Continuous

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00350425" target="_blank" >RIV/68407700:21240/22:00350425 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/S147474802100013X" target="_blank" >https://doi.org/10.1017/S147474802100013X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S147474802100013X" target="_blank" >10.1017/S147474802100013X</a>

Result language
angličtina
Original language name
Normal Functionals on Lipschitz Spaces are Weak* Continuous
Original language description
Let Lip_0(M) be the space of Lipschitz functions on a complete metric space M that vanish at a base point. We prove that every normal functional in Lip_0(M)* is weak* continuous; that is, in order to verify weak* continuity it suffices to do so for bounded monotone nets of Lipschitz functions. This solves a problem posed by N. Weaver. As an auxiliary result, we show that the series decomposition developed by N. J. Kalton for functionals in the predual of Lip_0(M) can be partially extended to Lip_0(M)*.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ18-00960Y" target="_blank" >GJ18-00960Y: Selected topics in non-linear functional analysis and approximation theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)