By Nigel J. Kalton
The overall challenge addressed during this paintings is to represent the attainable Banach lattice buildings separable Banach house can have. the elemental questions of forte of lattice constitution for functionality areas were studied prior to, yet right here the method makes use of random degree representations for operators in a new technique to receive extra strong conclusions. a standard result's the subsequent: If $X$ is a rearrangement-invariant area on $[0,1]$ now not equivalent to $L_2$, and if $Y$ is an order-continuous Banach lattice which has a complemented subspace isomorphic as a Banach house to $X$, then $Y$ has a complemented sublattice that's isomorphic to $X$ (with considered one of attainable lattice structures). New examples also are given of areas with a special lattice constitution.
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