Dunford–Pettis type properties and the Grothendieck property for function spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00532217" target="_blank" >RIV/67985840:_____/20:00532217 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s13163-019-00336-9" target="_blank" >https://doi.org/10.1007/s13163-019-00336-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13163-019-00336-9" target="_blank" >10.1007/s13163-019-00336-9</a>

Result language

angličtina

Original language name

Dunford–Pettis type properties and the Grothendieck property for function spaces

Original language description

For a Tychonoff space X, let Ck(X) and Cp(X) be the spaces of real-valued continuous functions C(X) on X endowed with the compact-open topology and the pointwise topology, respectively. If X is compact, the classic result of A. Grothendieck states that Ck(X) has the Dunford–Pettis property and the sequential Dunford–Pettis property. We extend Grothendieck’s result by showing that Ck(X) has both the Dunford–Pettis property and the sequential Dunford–Pettis property if X satisfies one of the following conditions: (1) X is a hemicompact space, (2) X is a cosmic space (= a continuous image of a separable metrizable space), (3) X is the ordinal space [0 , κ) for some ordinal κ, or (4) X is a locally compact paracompact space. We show that if X is a cosmic space, then Ck(X) has the Grothendieck property if and only if every functionally bounded subset of X is finite. We prove that Cp(X) has the Dunford–Pettis property and the sequential Dunford–Pettis property for every Tychonoff space X, and Cp(X) has the Grothendieck property if and only if every functionally bounded subset of X is finite.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

Revista Mathématica Complutense

ISSN

1139-1138

e-ISSN

—

Volume of the periodical

33

Issue of the periodical within the volume

3

Country of publishing house

ES - SPAIN

Number of pages

14

Pages from-to

871-884

UT code for WoS article

000567467200011

EID of the result in the Scopus database

2-s2.0-85076085610