Convex Komlós sets in Banach function spaces
نویسندگان
چکیده
منابع مشابه
Some results on functionally convex sets in real Banach spaces
We use of two notions functionally convex (briefly, F--convex) and functionally closed (briefly, F--closed) in functional analysis and obtain more results. We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$, then $bigcup_{alphain I}A_{alpha}$ is F--convex. Moreover, we introduce new definition o...
متن کاملFunctionally closed sets and functionally convex sets in real Banach spaces
Let $X$ be a real normed space, then $C(subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)subseteq Bbb R $ is convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)subseteq Bbb R $ is closed for all bounded linear transformations $Tin B(X,R)$. We improve the Krein-Milman theorem ...
متن کاملfunctionally closed sets and functionally convex sets in real banach spaces
let $x$ be a real normed space, then $c(subseteq x)$ is functionally convex (briefly, $f$-convex), if $t(c)subseteq bbb r $ is convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$ is functionally closed (briefly, $f$-closed), if $t(k)subseteq bbb r $ is closed for all bounded linear transformations $tin b(x,r)$. we improve the krein-milman theorem ...
متن کاملOn remotality for convex sets in Banach spaces
We show that every in nite dimensional Banach space has a closed and bounded convex set that is not remotal. This settles a problem raised by Sababheh and Khalil in [8].
متن کاملConvex Games in Banach Spaces
We study the regret of an online learner playing a multi-round game in a Banach space B against an adversary that plays a convex function at each round. We characterize the minimax regret when the adversary plays linear functions in terms of the Rademacher type of the dual of B. The cases when the adversary plays bounded and uniformly convex functions respectively are also considered. Our resul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.12.040