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Isomorphisms of some reflexive algebras

Jiankui LiZhidong Pan — 2008

Studia Mathematica

Suppose ℒ₁ and ℒ₂ are subspace lattices on complex separable Banach spaces X and Y, respectively. We prove that under certain lattice-theoretic conditions every isomorphism from algℒ₁ to algℒ₂ is quasi-spatial; in particular, if a subspace lattice ℒ of a complex separable Banach space X contains a sequence E i such that ( E i ) X , E i E i + 1 , and i = 1 E i = X then every automorphism of algℒ is quasi-spatial.

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