A new class of weakly countably determined Banach spaces

• Autorzy: K. K. Kampoukos , S. K. Mercourakis
• Języki publikacji: EN

Abstrakty

EN

A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing ℓ¹(ℕ) is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If K is a compact space, then the space C(K) is SWCD if and only if K is countable.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 46B20: Geometry and structure of normed linear spaces
• 03E15: Descriptive set theory
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 208
• Numer: 2
• Strony: 155-171

Daty

wydano

2010

Twórcy

autor

K. K. Kampoukos

• Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece

autor

S. K. Mercourakis

• University of Athens, Department of Mathematics, Panepistemiopolis, 15784 Athens, Greece

Identyfikatory

DOI

10.4064/fm208-2-3