J-subspace lattices and subspace M-bases

W. Longstaff; Oreste Panaia

Displaying similar documents to “J-subspace lattices and subspace M-bases”

Reflexivity of bilattices

Kamila Kliś-Garlicka (2013)

Czechoslovak Mathematical Journal

Similarity:

We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice $ℒ$ we may associate a bilattice $Σ_{ℒ}$ . Similarly, having a bilattice $Σ$ we may construct a subspace lattice $ℒ_{Σ}$ . Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.

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

Marek Wójtowicz (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.