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- W3198474184 abstract "A well-known classical result states that c0 is linearly embeddable in a Banach lattice if and only if it is lattice embeddable. Improving results of H.P. Lotz, H.P. Rosenthal and N. Ghoussoub, we prove that C[0,1] shares this property with c0. Furthermore, we show that any infinite-dimensional closed sublattice of C[0,1] is either lattice isomorphic to c0 or contains a closed sublattice isomorphic to C[0,1]. As a consequence, it is proved that for a separable Banach lattice X the following conditions are equivalent: X is linearly embeddable in a Banach lattice if and only if it is lattice embeddable; X is lattice embeddable into C[0,1]." @default.
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- W3198474184 date "2022-09-01" @default.
- W3198474184 modified "2023-10-14" @default.
- W3198474184 title "Linear versus lattice embeddings between Banach lattices" @default.
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- W3198474184 doi "https://doi.org/10.1016/j.aim.2022.108574" @default.
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