A Stone-Weierstrass theorem for Banach lattices

Rainer Nagel

Displaying similar documents to “A Stone-Weierstrass theorem for Banach lattices”

A local characterization of Banach lattices with order continuous norm

S. Bernau, H. Lacey (1976)

Studia Mathematica

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The lattice copies of $ℓ_{1}$ in Banach lattices

Marek Wójtowicz (2001)

Commentationes Mathematicae Universitatis Carolinae

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It is known that a Banach lattice with order continuous norm contains a copy of $ℓ_{1}$ if and only if it contains a lattice copy of $ℓ_{1}$ . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the $c_{0}$ - and $ℓ_{\infty}$ -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.