EmbeddingL 1 in a Banach lattice
Copyright policy )EmbeddingL 1 in a Banach lattice
We show that ifX is a Banach lattice containing no copy ofc0 and ifZ is a subspace ofX isomorphic toL1[0, 1] then (a)Z contains a subspaceZ0 isomorphic toL1 and complemented inX and (b)X contains a complemented sublattice isomorphic and lattice-isomorphic toL1.
- University of Illinois System United States
- University of Illinois at Urbana Champaign United States
Banach lattices, Geometry and structure of normed linear spaces, Banach Lattice, L1-Space, Classical Banach spaces in the general theory, Ordered topological linear spaces, vector lattices, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Embedding, Complemented Sublattice
Banach lattices, Geometry and structure of normed linear spaces, Banach Lattice, L1-Space, Classical Banach spaces in the general theory, Ordered topological linear spaces, vector lattices, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Embedding, Complemented Sublattice
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