Isomorphisms of some reflexive algebras

• Autorzy: Jiankui Li , Zhidong Pan
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L35: Nest algebras, CSL algebras
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 1
• Strony: 95-100

Daty

wydano

2008

Twórcy

autor

Jiankui Li

• Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P.R. China

autor

Zhidong Pan

• Department of Mathematics, Saginaw Valley State University, University Center, MI 48710, U.S.A.

Identyfikatory

DOI

10.4064/sm187-1-5