Article
| Title: | On the range of some elementary operators (English) |
| Author: | El Mouadine, Hamza |
| Author: | Faouzi, Abdelkhalek |
| Author: | Bouhafsi, Youssef |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 53-62 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | Let $L(H)$ denote the algebra of all bounded linear operators on a complex infinite dimensional Hilbert space $H$. For $A,B\in L(H)$, the generalized derivation $\delta_{A,B}$ and the multiplication operator $M_{A,B}$ are defined on $L(H)$ by $\delta_{A,B}(X)=AX-XB$ and $M_{A,B}(X)=AXB$. In this paper, we give a characterization of bounded operators $A$ and $B$ such that the range of $M_{A,B}$ is closed. We present some sufficient conditions for $\delta_{A,B}$ to have closed range. Some related results are also given. (English) |
| Keyword: | generalized derivation |
| Keyword: | elementary operator |
| Keyword: | generalized inverse |
| Keyword: | Kato spectrum |
| MSC: | 47A16 |
| MSC: | 47A30 |
| MSC: | 47B07 |
| MSC: | 47B20 |
| MSC: | 47B47 |
| DOI: | 10.14712/1213-7243.2025.004 |
| . | |
| Date available: | 2025-04-24T07:48:50Z |
| Last updated: | 2025-04-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152944 |
| . | |
| Reference: | [1] Anderson J. H., Foiaş C.: Properties which normal operators share with normal derivations and related operators.Pacific J. Math. 61 (1975), no. 2, 313–325. MR 0412889, 10.2140/pjm.1975.61.313 |
| Reference: | [2] Apostol C.: Inner derivations with closed range.Rev. Roumaine Math. Pures Appl. 21 (1976), no. 3, 249–265. MR 0410459 |
| Reference: | [3] Apostol C., Stampfli J.: On derivation ranges.Indiana Univ. Math. J. 25 (1976), no. 9, 857–869. MR 0412890 |
| Reference: | [4] Badea C., Mbekhta M.: Compressions of resolvents and maximal radius of regularity.Trans. Amer. Math. Soc. 351 (1999), no. 7, 2949–2960. MR 1621709, 10.1090/S0002-9947-99-02365-X |
| Reference: | [5] Caradus S. R.: Generalized Inverses and Operator Theory.Queen's Papers in Pure and Applied Mathematics, 50, Queen's University, Kingston, 1978. Zbl 0434.47003, MR 0523736 |
| Reference: | [6] Davis C., Rosenthal P.: Solving linear operator equations.Canadian J. Math. 26 (1974), 1384–1389. MR 0355649, 10.4153/CJM-1974-132-6 |
| Reference: | [7] Fialkow L. A.: Structural properties of elementary operators.in Elementary Operators and Applications, Blaubeuren, 1991, World Sci. Publ., River Edge, 1992, pages 55–113. MR 1183937 |
| Reference: | [8] Fialkow L. A., Herrero D. A.: Inner derivations with closed range in the Calkin algebra.Indiana Univ. Math. J. 33 (1984), no. 2, 185–211. MR 0733896, 10.1512/iumj.1984.33.33010 |
| Reference: | [9] Laursen K. B., Neumann M. M.: An Introduction to Local Spectral Theory.London Mathematical Society Monographs, New Series, 20, The Clarendon Press, Oxford University Press, New York, 2000. MR 1747914 |
| Reference: | [10] Mbekhta M.: Résolvant généralisé et théorie spectrale.J. Operator Theory 21 (1989), no. 1, 69–105 (French). MR 1002122 |
| Reference: | [11] Rosenblum M.: On the operator equation $BX-XA=Q$.Duke Math. J. 23 (1956), 263–269. MR 0079235, 10.1215/S0012-7094-56-02324-9 |
| Reference: | [12] Stampfli J. G.: On the range of a hyponormal derivation.Proc. Amer. Math. Soc. 52 (1975), 117–120. MR 0377575, 10.1090/S0002-9939-1975-0377575-X |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
