Extensions of vector-valued Baire one functions with preservation of points of continuity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00459546" target="_blank" >RIV/67985840:_____/16:00459546 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2016.04.052" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2016.04.052</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2016.04.052" target="_blank" >10.1016/j.jmaa.2016.04.052</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extensions of vector-valued Baire one functions with preservation of points of continuity

Popis výsledku v původním jazyce

We prove an extension theorem (with non-tangential limits) for vector-valued Baire one functions. Moreover, at every point where the function is continuous (or bounded), the continuity (or boundedness) is preserved. More precisely: Let H be a closed subset of a metric space X and let Z be a normed vector space. Let ... be a Baire one function. We show that there is a continuous function ... such that, for every ..., the non-tangential limit of g at a equals f(a)f(a) and, moreover, if f is continuous at ... (respectively bounded in a neighborhood of ...) then the extension ... is continuous at a (respectively bounded in a neighborhood of a). We also prove a result on pointwise approximation of vector-valued Baire one functions by a sequence of locally Lipschitz functions that converges “uniformly (or, “continuously) at points where the approximated function is continuous.

Název v anglickém jazyce

Extensions of vector-valued Baire one functions with preservation of points of continuity

Popis výsledku anglicky

We prove an extension theorem (with non-tangential limits) for vector-valued Baire one functions. Moreover, at every point where the function is continuous (or bounded), the continuity (or boundedness) is preserved. More precisely: Let H be a closed subset of a metric space X and let Z be a normed vector space. Let ... be a Baire one function. We show that there is a continuous function ... such that, for every ..., the non-tangential limit of g at a equals f(a)f(a) and, moreover, if f is continuous at ... (respectively bounded in a neighborhood of ...) then the extension ... is continuous at a (respectively bounded in a neighborhood of a). We also prove a result on pointwise approximation of vector-valued Baire one functions by a sequence of locally Lipschitz functions that converges “uniformly (or, “continuously) at points where the approximated function is continuous.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA14-07880S" target="_blank" >GA14-07880S: Metody teorie funkcí a Banachových algeber v teorii operátorů V.</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

442

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

138-148

Kód UT WoS článku

000376837100008

EID výsledku v databázi Scopus

2-s2.0-84964577841