A note on Asplund generated Banach spaces

• Autorzy: Fabian M. , Godefroy G. , Zizler V.
• Języki publikacji: EN

Abstrakty

EN

Assume that a Banach space X has density character Aleph[1] and that there is an Asplund space Y and a bounded linear operator T from Y onto a dense set in X. We show that such Y then can be chosen a reflexive space provided that X admits a projectional resolution of identity in each equivalent norm on X. We prove that the dual unit ball B[x*] in its weak star topology is a Corson compact provided that the norm of X is Gateaux differentiable and B[x*] is a Valdivia compact.

Słowa kluczowe

EN

asplund generating; Corson and Valdivia compacts; projectional resolution of the identity; weak compact generating; geometry structure normed linear space

PL

analiza funkcjonalna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 3
• Strony: 221--230
• Opis fizyczny: Bibliogr. 27 poz.,

Twórcy

autor

Fabian M.

autor

Godefroy G.

autor

Zizler V.