Ring isomorphisms and pentagon subspace lattices

If K, L and M are (closed) subspaces of a Banach space X satisfying K∩ M=(0), K∨ L= X and L⊂ M, then P={(0),K,L,M,X} is called a pentagon subspace lattice on X. Let P i be a pentagon subspace lattice on a complex Banach space X i , for i=1, 2. Then every ring isomorphism from Alg P 1 onto Alg P 2 is...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 367; pp. 59 - 66
Main Authors Li, Pengtong, Ma, Jipu
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 01.07.2003
Elsevier Science
Subjects
Algebra
Conjugate-linearity
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Pentagon subspace lattices
Quasi-spatiality
Ring isomorphisms
Sciences and techniques of general use
Pentagon subspace lattices
Conjugate-linearity
47B49
Quasi-spatiality
Ring isomorphisms
47L10
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Summary:If K, L and M are (closed) subspaces of a Banach space X satisfying K∩ M=(0), K∨ L= X and L⊂ M, then P={(0),K,L,M,X} is called a pentagon subspace lattice on X. Let P i be a pentagon subspace lattice on a complex Banach space X i , for i=1, 2. Then every ring isomorphism from Alg P 1 onto Alg P 2 is a quasi-spatially induced linear or conjugate-linear algebra isomorphism.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(02)00588-8