## Taiwanese Journal of Mathematics

### SINGLE ELEMENTS IN SOME REFLEXIVE ALGEBRA MODULES

Z. Dong

#### Abstract

In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in Alg$\mathcal{L}$-module $\mathcal{U}_{\phi}$ is initiated, where $\mathcal{L}$ is a completely distributive subspace lattice on a Banach space $\mathcal{X}$ and $\phi$ is an order homomorphism from $\mathcal{L}$ into $\mathcal{L}$. For a reflexive Banach space $\mathcal{X}$ and a positive integer $n$ (or $+\infty$), by virtue of the order homomorphism $\phi$ we give necessary and sufficient conditions for the existence of single elements of $\mathcal{U}_{\phi}$ of rank $n$ (or $+\infty$).

#### Article information

Source
Taiwanese J. Math., Volume 11, Number 1 (2007), 107-115.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404638

Digital Object Identifier
doi:10.11650/twjm/1500404638

Mathematical Reviews number (MathSciNet)
MR2304008

Zentralblatt MATH identifier
1143.47059

Subjects
Primary: 47L75: Other nonselfadjoint operator algebras

#### Citation

Dong, Z. SINGLE ELEMENTS IN SOME REFLEXIVE ALGEBRA MODULES. Taiwanese J. Math. 11 (2007), no. 1, 107--115. doi:10.11650/twjm/1500404638. https://projecteuclid.org/euclid.twjm/1500404638