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2010/2011 Two-Norm Convergence in the Lp Spaces
Ch. Rini Indrati
Real Anal. Exchange 36(1): 55-64 (2010/2011).


We have characterized the spaces $X$ for which the smallest $z$-ideal containing $c_\infty$ is prime. It turns out that $c_\infty$ is a $z$-ideal in $C(X)$ if and only if every zero-set contained in an open locally compact $\sigma$-compact set is compact. Some interesting ideals related to $c_\infty$ are introduced and corresponding to the relations between these ideals and $c_\infty$, topological spaces $X$ are characterized. Some compactness concepts are explicitly stated in terms of ideals related to $c_\infty$. Finally we have shown that a $\sigma$-compact space $X$ is Baire if and only if every ideal containing $c_\infty$ is essential.


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Ch. Rini Indrati. "Two-Norm Convergence in the Lp Spaces." Real Anal. Exchange 36 (1) 55 - 64, 2010/2011.


Published: 2010/2011
First available in Project Euclid: 14 March 2011

zbMATH: 1225.46022
MathSciNet: MR3016403

Primary: 26A04 , 26A39
Secondary: 26A05

Keywords: $L_p$, $1 \le p \le \infty$\\ , representation , two-norm

Rights: Copyright © 2010 Michigan State University Press

Vol.36 • No. 1 • 2010/2011
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