A new class of weakly countably determined Banach spaces

K. K. Kampoukos, and S. K. Mercourakis. "A new class of weakly countably determined Banach spaces." Fundamenta Mathematicae 208.2 (2010): 155-171. <http://eudml.org/doc/283032>.

@article{K2010,
abstract = {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.},
author = {K. K. Kampoukos, S. K. Mercourakis},
journal = {Fundamenta Mathematicae},
keywords = {WCD; SWCD Banach spaces; countably dermined space; strongly countably determined space; weakly countably determined spaces},
language = {eng},
number = {2},
pages = {155-171},
title = {A new class of weakly countably determined Banach spaces},
url = {http://eudml.org/doc/283032},
volume = {208},
year = {2010},
}

TY - JOUR
AU - K. K. Kampoukos
AU - S. K. Mercourakis
TI - A new class of weakly countably determined Banach spaces
JO - Fundamenta Mathematicae
PY - 2010
VL - 208
IS - 2
SP - 155
EP - 171
AB - 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.
LA - eng
KW - WCD; SWCD Banach spaces; countably dermined space; strongly countably determined space; weakly countably determined spaces
UR - http://eudml.org/doc/283032
ER -