Twisted properties of banach spaces

Jesús M. F. Castillo, Manuel Gonzáles, Anatolij M. Plichko, David Yost

Abstract


If $\mathcal P$, $\mathcal Q$ are two linear topological properties, say that a Banach space $X$ has the property $\mathcal P$-by-$\mathcal Q$ (or is a $\mathcal P$-by-$\mathcal Q$ space) if $X$ has a subspace $Y$ with property $\mathcal P$ such that the corresponding quotient $X/Y$ has property $\mathcal Q$. The choices $\mathcal P,\mathcal Q \in\{\hbox{separable, reflexive}\}$ lead naturally to some new results and new proofs of old results concerning weakly compactly generated Banach spaces. For example, every extension of a subspace of $L_1(0,1)$ by a WCG space is WCG. They also give a simple new example of a Banach space property which is not a 3-space property but whose dual is a 3-space property.

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DOI: http://dx.doi.org/10.7146/math.scand.a-14339

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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