Existence of indecomposable members in indecomposable spaces of operators |
| |
Authors: | Alexey I Popov |
| |
Institution: | 1.Department of Mathematics and Computer Science,University of Lethbridge,Lethbridge, Alberta,Canada |
| |
Abstract: | In this paper we prove that if S is a set of operators acting on a separable L p -space X, 1 ≤ p < ∞ (or, more generally, on any separable Köthe function space) such that S is indecomposable (that is, no non-trivial subspace of X of the form L p (A), where A is measurable, is a common S-invariant subspace), then \(\overline {span} \) S admits an indecomposable operator. As applications, we obtain some new results about transitive algebas on separable Hilbert spaces, as well as an extension of the simultaneous Wielandt theorem to semigroups of operators acting on separable L p -spaces. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|