Strict U-Ideals and U-Summands in Banach Spaces
- Autores: Trond A. Abrahamsen
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 114, Nº 2, 2014, págs. 216-225
- Idioma: inglés
- DOI: 10.7146/math.scand.a-17108
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Resumen
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.
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