Abstract
In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in AlgL-module Uφ is initiated, where L is a completely distributive subspace lattice on a Banach space X and φ is an order homomorphism from L into L. For a reflexive Banach space X and a positive integer n (or +∞), by virtue of the order homomorphism φ we give necessary and sufficient conditions for the existence of single elements of Uφ of rank n (or +∞).
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