Almost disjoint families of countable sets and separable complementation properties

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00391353" target="_blank" >RIV/67985840:_____/13:00391353 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2013.01.008" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2013.01.008</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2013.01.008" target="_blank" >10.1016/j.jmaa.2013.01.008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Almost disjoint families of countable sets and separable complementation properties

Popis výsledku v původním jazyce

We study the separable complementation property (SCP) and its natural variations in Banach spaces of continuous functions over compacta KA induced by almost disjoint families A of countable subsets of uncountable sets. For these spaces, we prove among other things that C(KA) has the controlled variant of the separable complementation property if and only if C(KA) is indelöf in the weak topology if and only if KA is monolithic. We give an example of A for which C(KA) has the SCP while KA is not monolithic and an example of a space C(KA) with controlled and continuous SCP which has neither a projectional skeleton nor a projectional resolution of the identity. Finally, we describe the structure of almost disjoint families of cardinality?1 which induce monolithic spaces of the form KA: they can be obtained from countably many ladder systems and pairwise disjoint families by applying simple operations.

Název v anglickém jazyce

Almost disjoint families of countable sets and separable complementation properties

Popis výsledku anglicky

We study the separable complementation property (SCP) and its natural variations in Banach spaces of continuous functions over compacta KA induced by almost disjoint families A of countable subsets of uncountable sets. For these spaces, we prove among other things that C(KA) has the controlled variant of the separable complementation property if and only if C(KA) is indelöf in the weak topology if and only if KA is monolithic. We give an example of A for which C(KA) has the SCP while KA is not monolithic and an example of a space C(KA) with controlled and continuous SCP which has neither a projectional skeleton nor a projectional resolution of the identity. Finally, we describe the structure of almost disjoint families of cardinality?1 which induce monolithic spaces of the form KA: they can be obtained from countably many ladder systems and pairwise disjoint families by applying simple operations.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topologické a geometrické vlastnosti Banachových prostorů a operátorových algeber</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

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

401

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

939-949

Kód UT WoS článku

000315425900042

EID výsledku v databázi Scopus

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