Isomorphisms of some reflexive algebras

Jiankui Li, and Zhidong Pan. "Isomorphisms of some reflexive algebras." Studia Mathematica 187.1 (2008): 95-100. <http://eudml.org/doc/284681>.

@article{JiankuiLi2008,
abstract = {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.},
author = {Jiankui Li, Zhidong Pan},
journal = {Studia Mathematica},
keywords = {subspace lattice; isomorphism; quasi-spatial; reflexive; sequentially dense},
language = {eng},
number = {1},
pages = {95-100},
title = {Isomorphisms of some reflexive algebras},
url = {http://eudml.org/doc/284681},
volume = {187},
year = {2008},
}

TY - JOUR
AU - Jiankui Li
AU - Zhidong Pan
TI - Isomorphisms of some reflexive algebras
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 1
SP - 95
EP - 100
AB - 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.
LA - eng
KW - subspace lattice; isomorphism; quasi-spatial; reflexive; sequentially dense
UR - http://eudml.org/doc/284681
ER -