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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GA14-07880S" target="_blank" >GA14-07880S: Methods of function theory and Banach algebras in operator theory V.</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Volume of the periodical

442

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

138-148

UT code for WoS article

000376837100008

EID of the result in the Scopus database

2-s2.0-84964577841