Strictly singular operators on Lp spaces and interpolation
| dc.contributor.author | Hernández, Francisco L. | |
| dc.contributor.author | Semenov, Evgeny M. | |
| dc.contributor.author | Tradacete Pérez, Pedro | |
| dc.date.accessioned | 2023-06-20T00:14:32Z | |
| dc.date.available | 2023-06-20T00:14:32Z | |
| dc.date.issued | 2010-02 | |
| dc.description.abstract | We study the class Vp of strictly singular non-compact operators on Lp spaces. This allows us to obtain interpolation results for strictly singular operators on Lp spaces. Given 1 ≤ p < q ≤ ∞, it is shown that if an operator T bounded on Lp and Lq is strictly singular on Lr for some p ≤ r ≤ q, then it is compact on Ls for every p < s < q. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MICINN | |
| dc.description.sponsorship | Santander/Complutense | |
| dc.description.sponsorship | Russian Fund of Basic Research | |
| dc.description.sponsorship | MEC | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15986 | |
| dc.identifier.doi | 10.1090/S0002-9939-09-10089-8 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.officialurl | http://www.ams.org/journals/proc/2010-138-02/home.html | |
| dc.identifier.relatedurl | http://www.ams.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42256 | |
| dc.issue.number | 2 | |
| dc.journal.title | Proceedings of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 686 | |
| dc.page.initial | 675 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | MTM2008-02652 | |
| dc.relation.projectID | PR34/07-15837 | |
| dc.relation.projectID | 08-01-00226-a | |
| dc.relation.projectID | AP-2004-4841 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.cdu | 517.982.2 | |
| dc.subject.cdu | 517.518.85 | |
| dc.subject.keyword | Strictly singular operator | |
| dc.subject.keyword | Lp space | |
| dc.subject.keyword | interpolation | |
| dc.subject.keyword | ideals | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Strictly singular operators on Lp spaces and interpolation | |
| dc.type | journal article | |
| dc.volume.number | 138 | |
| dcterms.references | Y.A. Abramovich, C. D. Aliprantis. An invitation to operator theory. Graduate Studies in Mathematics, 50. American Mathematical Society, Providence, RI, 2002. D. Alspach, E. Odell. Lp spaces. Handbook of the geometry of Banach spaces, Vol. I, 123–159, North-Holland, Amsterdam, 2001. O. J. Beucher. On interpolation of strictly (co-)singular linear operators. Proc. Roy. Soc. Edinb. A 112 (1989), 263–269. J. W. Calkin. Two-sided ideals and congruences in the ring of bounded operators in Hilbert space. Annals of Math. (2) 42, 4 (1941), 839–873. V. Caselles, M. González. Compactness properties of strictly singular operators in Banach lattices. Semesterbericht Funktionalanalysis. Tübingen, Sommersemester (1987), 175–189. F. Cobos, A. Manzano, A. Martínez, P. Matos. On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals. Proc. Roy. Soc. Edinb. A 130 (2000), 971–989. L. Dor. On projections in L1. Annals of Math. (2) 102 (1975), 463–474. I. T. Gohberg, A. S. Markus, I. A. Feldman. On normal solvable operators and related ideals. Amer. Math. Soc. Transl. (2), Vol. 61, Amer. Math. Soc., Providence, RI, 1967, 63–84. S. Goldberg. Unbounded linear operators. Theory and applications. Dover Publications, Mineola, NY, 2006. S. Heinrich. Closed operator ideals and interpolation. J. Funct. Analysis 35 (1980), 397–411. M. I. Kadeč, A. Pelczyński. Bases, lacunary sequences and complemented subspaces in the spaces Lp. Studia Math. 21 (1962), 161–176. T. Kato. Perturbation theory for nullity deficiency and order quantities of linear operators. J. Analyse. Math. 6 (1958), 273–322. M. A. Krasnosel’skiĭ. On a theorem of M. Riesz. Dokl. Akad. Nauk SSSR 131, 246–248 (in Russian); translated as Soviet Math. Dokl. 1 (1960), 229–231. M. A. Krasnosel’skiĭ, P. P. Zabreĭko, E. I. Pustyl’nik, P. E. Sobolevskiĭ. Integral operators in spaces of summable functions. Noordhoff International Publishing, Leiden, 1976. J. Lindenstrauss, L. Tzafriri. Classical Banach spaces. I. Springer-Verlag, Berlin-New York, 1977. M. Lindström, E. Saksman, H.-O. Tylli. Strictly singular and cosingular multiplications. Canad. J. Math. 57 (2005), 1249–1278. V. D. Milman. Operators of classes C0 and C∗0 . Functions theory, functional analysis and appl., Vol. 10 (1970), 15–26 (in Russian). A. Pelczyński. On strictly singular and strictly cosingular operators, I and II. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 31–41. A. Pelczyński, H. P. Rosenthal. Localization techniques in Lp spaces. Studia Math. 52 (1974/75), 263–289. C. J. Read. Strictly singular operators and the invariant subspace problem. Studia Math. 132 (1999), 203–226. W. Rudin. Functional analysis. McGraw-Hill, New York, 1973. E. M. Semënov, F. A. Sukochev. The Banach–Saks index. Sbornik Mathematics 195 (2004), 263–285. L. Weis. On perturbations of Fredholm operators in Lp(μ)-spaces. Proc. Amer. Math. Soc. 67 (1977), 287–292. L. Weis. Integral operators and changes of density. Indiana Univ. Math. J. 31 (1982), 83–96. R. J. Whitley. Strictly singular operators and their conjugates. Trans. Amer. Math. Soc. 113 (1964), 252–261. | |
| dspace.entity.type | Publication |
Download
Original bundle
1 - 1 of 1