1. Large Perturbations of Nest Algebras
- Author
-
Davidson, Kenneth R.
- Subjects
Mathematics - Operator Algebras ,Mathematics - Functional Analysis ,Primary 47L35, Secondary 47B02, 47A55 - Abstract
Let $\mathcal{M}$ and $\mathcal{N}$ be nests on separable Hilbert space. If the two nest algebras are distance less than 1 ($d(\mathcal{T}(\mathcal{M}),\mathcal{T}(\mathcal{N})) < 1$), then the nests are distance less than 1 ($d(\mathcal{M},\mathcal{N})<1$). If the nests are distance less than 1 apart, then the nest algebras are similar, i.e. there is an invertible $S$ such that $S\mathcal{M} = \mathcal{N}$, so that $S \mathcal{T}(\mathcal{M})S^{-1} = \mathcal{T}(\mathcal{N})$. However there are examples of nests closer than 1 for which the nest algebras are distance 1 apart., Comment: Minor changes including a correction in the proof of Theorem 2.2. To appear in Integral Equations & Operator Theory
- Published
- 2024