Isomorphisms of some reflexive algebras

Jiankui Li ¹   ; Zhidong Pan ²

¹ Department of Mathematics East China University of Science and Technology Shanghai 200237, P.R. China
² Department of Mathematics Saginaw Valley State University University Center, MI 48710, U.S.A.

Studia Mathematica, Tome 187 (2008) no. 1, pp. 95-100

Résumé

Suppose $\mathcal L_1$ and $\mathcal L_2$ are subspace lattices on complex separable Banach spaces $X$ and $Y$, respectively. We prove that under certain lattice-theoretic conditions every isomorphism from $\mathop{\rm alg}\mathcal L_1$ to $\mathop{\rm alg}\mathcal L_2$ is quasi-spatial; in particular, if a subspace lattice $\mathcal L$ 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 $\bigvee_{i=1}^{\infty} E_i = X$ then every automorphism of $\mathop{\rm alg} \mathcal L$ is quasi-spatial.

Détail

DOI : 10.4064/sm187-1-5

Keywords: suppose mathcal mathcal subspace lattices complex separable banach spaces respectively prove under certain lattice theoretic conditions every isomorphism mathop alg mathcal mathop alg mathcal quasi spatial particular subspace lattice mathcal complex separable banach space contains sequence neq subseteq bigvee infty every automorphism mathop alg mathcal quasi spatial