Local resolvents of operators with one-dimensional self-commutator
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- by Constantin Apostol and Kevin Clancey PDF
- Proc. Amer. Math. Soc. 58 (1976), 158-162 Request permission
Abstract:
Let $T = H + iJ$ be an irreducible operator on a Hilbert space with one-dimensional self-commutator. It is known that the selfadjoint operator $H$ is absolutely continuous. Let ${E_H}$ denote the absolutely continuous support of $H$. In this note the following theorem is proven: Theorem. If there exists a real number $p$ such that $\operatorname {ess} {\inf }{E_H} < p < \operatorname {ess} \sup {E_H}$ and $\int _{{E_H}}^{} {|t - p{|^{ - 1}}dt < \infty }$, then the operator $T$ has a nontrivial invariant subspace.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 158-162
- MSC: Primary 47A15; Secondary 47B47
- DOI: https://doi.org/10.1090/S0002-9939-1976-0410418-5
- MathSciNet review: 0410418