Large Perturbations of Nest Algebras
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.03317
- arXiv:
- arXiv:2408.03317
- Bibcode:
- 2024arXiv240803317D
- Keywords:
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- Mathematics - Operator Algebras;
- Mathematics - Functional Analysis;
- Primary 47L35;
- Secondary 47B02;
- 47A55
- E-Print:
- Minor changes including a correction in the proof of Theorem 2.2. To appear in Integral Equations &