Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces
| dc.contributor.author | Jiménez Sevilla, María Del Mar | |
| dc.contributor.author | Lajara, Sebastián | |
| dc.date.accessioned | 2023-06-22T12:28:05Z | |
| dc.date.available | 2023-06-22T12:28:05Z | |
| dc.date.issued | 2022-06 | |
| dc.description.abstract | We obtain several extensions of a theorem of Shevchik which asserts that if R is a proper dense operator range in a separable Banach space E, then there exists a compact, one-to-one and dense-range operator T : E → E such that T(E) ∩ R = {0}, and some results of Chalendar and Partington concerning the existence of compact, one-to-one and dense-range endomorphisms on a separable Banach space E which leave invariant a given closed subspace Y ⊂ E, or more generally, a countable increasing chain of closed subspaces of E. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/75378 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/72584 | |
| dc.language.iso | eng | |
| dc.relation.projectID | PGC2018-097286-B-I00; MTM2017-86182-P | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.982.22 | |
| dc.subject.keyword | Separable Banach spaces | |
| dc.subject.keyword | Nuclear operators | |
| dc.subject.keyword | Operator ranges | |
| dc.subject.keyword | Invariant subspaces | |
| dc.subject.keyword | Chains of subspaces | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces | |
| dc.type | journal article | |
| dcterms.references | [1] Y. A. Abramovich and C. D. Aliprantis, An invitation to Operator Theory. Graduate Studies in Mathematics vol. 50, Amer. Math. Soc., Providence, Rhode Island (2002). [2] G. Bennet and N. Kalton, Inclusion theorems for K-spaces, Canadian J. of Math. 25 (1973), 511-524. [3] J. M. Borwein and D. W. Tingley, On supportless convex sets, Proc. Amer. Math. Soc. 94 (1985), 471-476. [4] J. B. Conway, A Course in Functional Analysis. Graduate Texts in Mathematics, Springer-Verlag, New York (1990). [5] R. W. Cross, On the continuous linear image of a Banach space, J. Austral. Math. Soc. (Series A) 29 (1980), 219-234. [6] R. W. Cross and V. Shevchik, Disjointness of operator ranges, Quaest. Math. 21 (1998), 247-260. [7] I. Chalendar and J. Partington, An image problem for compact operators, Proc. Amer. Math. Soc. 134 (5) (2005), 1391-1396. [8] L. Drewnowski, A solution to a problem of De Wilde and Tsirulnikov, Manuscripta Math. 37 (1) (1982), 61-64. [9] A. F. M. ter Elst and M. Sauter, Nonseparability and von Neumann's theorem for domains of unbounded operators, J. Operator Theory 75 (2016), 367-386. [10] M. Fabian, P. Habala, P. Hajek, V. Montesinos, V. Zizler, Banach Space Theory: The basis for linear and nonlinear analysis. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer, New York, 2011 [11] P. A. Fillmore and J. P. Williams, On operator ranges, Adv. Math. 7 (1971), 254-281. [12] V. P. Fonf, On a property of families of imbedded Banach spaces, Teor. Funktsii Funktionsal Anal. i Prilozen 55 (1991), 140-145. [13] V. P. Fonf, S. Lajara, S. Troyanski and C. Zanco, Operator ranges and quasicomplemented subspaces of Banach spaces, Studia Math. 248 (2) (2019), 203-216. [14] S. Grivaux, Construction of operators with a prescribed behaviour, Arch. Math. 81 (2003), 291-299. [15] P. Hájek, V. Montesinos, J. Vanderwerff and V. Zizler, Biorthogonal systems in Banach spaces. CMS Books in Mathematics, Springer (2008). [16] D. Kitson and R.M. Timoney, Operator ranges and spaceability, J. Math. Anal. Appl. 378 (2) (2011) 680-686. [17] G. W. Mackey, Note on a theorem of Murray, Bull. Amer. Math. Soc. 52 (1946), 322-325. [18] A. N. Plichko, Some remarks on operator ranges (Russian), Teor. Funktsii Funktsional. Anal. i Prilozen. 53 (1990), 69-70. (English translation in J. Soviet Math. 58 (1992), 540-541). [19] V. Shevchik, On subspaces of a Banach space that coincide with the ranges of continuous linear operators (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 817-819. [20] I. Singer, On biorthogonal systems and total sequences of functionals, Math. Ann. 193 (1971), 183-188. [21] I. Singer, On biorthogonal systems and total sequences of functionals II, Math. Ann. 201 (1973), 1-8. [22] I. Singer, Bases in Banach spaces II, Springer-Verlag, Berlin (1981). [23] B. R. Yahaghi, On injective or dense-range operators leaving a given chain of subspaces invariant, Proc. Amer. Math. Soc. 132 (4) (2004), 1059-1066. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 | |
| relation.isAuthorOfPublication.latestForDiscovery | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 |
