1Aalesund University College Service Box 17 N-6025 Ålesund, Norway 2Department of Mathematics University of Agder Serviceboks 422 4604 Kristiansand, Norway
Studia Mathematica, Tome 195 (2009) no. 3, pp. 275-285
We study strict u-ideals in Banach spaces. A Banach space $X$ is a strict u-ideal in its bidual when the canonical decomposition $X^{***} = X^* \oplus X^\perp $ is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if $X$ is a strict u-ideal in a Banach space $Y$ then $X$ contains $c_0$. We also show that $\ell _\infty $ is not a u-ideal.
Keywords:
study strict u ideals banach spaces banach space strict u ideal its bidual canonical decomposition *** * oplus perp unconditional characterize banach spaces which strict u ideals their bidual strict u ideal banach space contains ell infty u ideal
Affiliations des auteurs :
Vegard Lima
1
;
Åsvald Lima
2
1
Aalesund University College Service Box 17 N-6025 Ålesund, Norway
2
Department of Mathematics University of Agder Serviceboks 422 4604 Kristiansand, Norway
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Vegard Lima; Åsvald Lima. Strict u-ideals in Banach spaces. Studia Mathematica, Tome 195 (2009) no. 3, pp. 275-285. doi: 10.4064/sm195-3-6
