Operators with connected spectrum + compact operators = strongly irreducible operators (Q1974186)
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scientific article; zbMATH DE number 1439322
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Operators with connected spectrum + compact operators = strongly irreducible operators |
scientific article; zbMATH DE number 1439322 |
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Operators with connected spectrum + compact operators = strongly irreducible operators (English)
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8 August 2001
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Let \(L(H)\) be the algebra of all bounded linear operators acting on a complex, separable, infinite-dimensional Hilbert space \(H\). An operator \(T\in L(H)\) is said to be strongly irreducible if it does not commute with any nontrivial idempotents. It is proved that each operator \(T\in L(H)\) with connected spectrum can be represented as the sum of a strongly irreducible operator and a compact operator.
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operators in Hilbert spase
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structure properties
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strongly irreducible
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sum of a strongly irreducible operator and a compact operator
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