Isomorphisms of some reflexive algebras

Jiankui Li; Zhidong Pan

Jiankui Li ; Zhidong Pan

Studia Mathematica, Tome 187 (2008), p. 95-100 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $(E_{i}) ₋ \neq X$ , $E_{i} \subseteq E_{i + 1}$ , and $⋁_{i = 1}^{\infty} E_{i} = X$ then every automorphism of algℒ is quasi-spatial.

Publié le : 2008-01-01

Zbl 1148.47051

EUDML-ID : urn:eudml:doc:284681

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     title = {Isomorphisms of some reflexive algebras},
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     year = {2008},
     pages = {95-100},
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Jiankui Li; Zhidong Pan. Isomorphisms of some reflexive algebras. Studia Mathematica, Tome 187 (2008) pp. 95-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-1-5/