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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Isomorphisms of some reflexive algebras

### Tom 187 / 2008

Studia Mathematica 187 (2008), 95-100 MSC: Primary 47B47, 47L35. DOI: 10.4064/sm187-1-5

#### Streszczenie

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.

#### Autorzy

• Jiankui LiDepartment of Mathematics
East China University of Science and Technology
Shanghai 200237, P.R. China
e-mail
• Zhidong PanDepartment of Mathematics
Saginaw Valley State University
University Center, MI 48710, U.S.A.
e-mail

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