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http://hdl.handle.net/10662/16990
Title: | Conditions ensuring T ⎺¹ (Y ) ⊂ Y |
Authors: | Medková, Dagmar |
Keywords: | Theorem of operator;Teorema de operadores |
Issue Date: | 2005 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | The following theorem is the main result of the paper: Let X be a complex Banach space and 𝑇 ∈ L(X). Suppose that 0 lies at the unbounded component of the set of those λ such that λI − 𝑇 is a Fredholm operator. Let Y be a dense subspace of the dual space X′ and S be a closed operator from Y to X such that 𝑇 ′( Y ) ⊂ Y and 𝑇 S𝓎 = ST ′𝓎 for each 𝓎 ∈ Y . Then for each vector 𝓍 ∈ X′, 𝑇 ′𝓍 ∈ Y𝓍 if and only if 𝓍 ∈ Y . |
URI: | http://hdl.handle.net/10662/16990 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 20, nº 1 (2005) |
Files in This Item:
File | Description | Size | Format | |
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2605-5686_20_1_43.pdf | 138,53 kB | Adobe PDF | View/Open | |
2605-5686_20_1_43_Abstract.pdf | 66,75 kB | Adobe PDF | View/Open |
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