| Автор | Albrecht, Ernst |
| Дата выпуска | 1982 |
| dc.description | Let H be a complex Hilbert space and denote by B(H) the Banach algebra of all bounded linear operators on H. In [5; 6] J. Ph. Labrousse proved that every operator S∈B(H) which is spectral in the sense of N. Dunford (see [3]) is similar to a T∈B(H) with the following propertyConversely, he showed that given an operator S∈B(H) such that its essential spectrum (in the sense of [5; 6]) consists of at most one point and such that S is similar to a T∈B(H) with the property (1), then S is a spectral operator. This led him to the conjecture that an operator S∈B(H) is spectral if and only if it is similar to a T∈B(H) with property (1). The purpose of this note is to prove this conjecture in the case of operators which are decomposable in the sense of C. Foias (see [2]). |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Glasgow Mathematical Journal Trust 1982 |
| Название | A characterization of spectral operators on Hilbert spaces |
| Тип | research-article |
| DOI | 10.1017/S0017089500004821 |
| Electronic ISSN | 1469-509X |
| Print ISSN | 0017-0895 |
| Журнал | Glasgow Mathematical Journal |
| Том | 23 |
| Первая страница | 91 |
| Последняя страница | 95 |
| Аффилиация | Albrecht Ernst; Universität des Saarlandes |
| Выпуск | 1 |
