Open AccessStrict U-Ideals and U-Summands in Banach Spaces
Author(s) -
Trond A. Abrahamsen
Publication year - 2014
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-17108
Subject(s) - mathematics , banach space , unit sphere , combinatorics , ideal (ethics) , ball (mathematics) , unit (ring theory) , space (punctuation) , dual (grammatical number) , pure mathematics , mathematical analysis , epistemology , philosophy , linguistics , art , mathematics education , literature
For a strict u-ideal $X$ in a Banach space $Y$ we show that the set of points in the dual unit ball $B_{X^{\ast}}$, strongly exposed by points in the range $\it TY$ of the unconditional extension operator $T$ from $Y$ into the bidual $X^{\ast\ast}$ of $X$, is contained in the weak$^{\ast}$ denting points in $B_{X^{\ast}}$. We also prove that a u-embedded space is a u-summand if and only if it contains no copy of $c_0$ if and only if it is weakly sequentially complete.