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Displaying similar documents to “On countability of the spectrum of Banach space valued weakly almost-periodic functions”

A new class of weakly countably determined Banach spaces

K. K. Kampoukos, S. K. Mercourakis (2010)

Fundamenta Mathematicae

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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.