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Completely Indecomposable Operators and a Uniqueness Theorem of Cartwright–Levinson Type: Addendum to

✍ Scribed by A. Atzmon; M. Sodin

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 72 KB
Volume: 175
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3621

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✦ Synopsis

The purpose of this note is to show that the answers to Problems 2, 3, and 5 in [1] are positive, even under weaker assumptions. Keeping the notations of [1], we have Theorem 1. If : is a positive sequence on Z + which converges to a nonzero limit, then the operator A(:) has a proper invariant subspace.

l 2 (Z + ). As

📜 SIMILAR VOLUMES

Completely Indecomposable Operators and

Completely Indecomposable Operators and a Uniqueness Theorem of Cartwright–Levinson Type

✍ A. Atzmon; M. Sodin 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 224 KB

A bounded linear operator T on a complex Hilbert space will be called completely indecomposable if its spectrum is not a singleton, and is included in the spectrum of the restrictions of T and T \* to any of their nonzero invariant subspaces. Two classes of completely indecomposable operators are co