On the coincidence of Pettis and McShane integrals and Hilbert generated spaces

0351199 - MÚ 2011 RIV CZ eng A - Abstrakt
Fabian, Marián
On the coincidence of Pettis and McShane integrals and Hilbert generated spaces.
Abstract book of CDEIT 2010. Brno: Masarykova univerzita, 2010 - (Došlá, Z.; Mařík, R.; Hilscher, R.; Šremr, J.). s. 21-22. ISBN 978-80-210-5289-5.
[Colloquium on differential equations and integration theory. 14.10.2010-17.10.2010, Křtiny]
Grant CEP: GA AV ČR IAA100190901
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: Hilbert spaces * Pettis and McShane integrals
Kód oboru RIV: BA - Obecná matematika

A Banach space X is called weakly compactly generated if it contains a weakly compact set which is linearly dense in it. X is called Hilbert generated provided that there are a Hilbert space Y and a linear bounded mapping from Y into X whose range is dense in X. A compact space is called Eberlein (uniform Eberlein) if it can be continuously injected into a Banach space (into a Hilbert space) provided with the weak topology. We recall well known facts that a compact space K is Eberlein (uniform Eberlein) if and only if the corresponding Banach space C(K) is weakly compactly generated (Hilbert generated).
Trvalý link: http://hdl.handle.net/11104/0191002