On Strictly Singular and Strictly Cosingular Embeddings Between Banach Lattices of Functions

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Cambridge Univ Press
Google Scholar
Research Projects
Organizational Units
Journal Issue
Let E be a Banach function lattice such that L1[0; 1] ,! E ,! L1[0; 1]. We characterize the strict singularity of the embedding L1[0; 1] ,! E and the strict cosingularity of E ,! L1[0; 1] in terms of functionals de_ned by using characteristic functions.
Unesco subjects
S. V. Astashkin. Disjointly strictly singular inclusions of symmetric spaces. Math. Notes 65 (1999), 3{14. C. Bennett and R. Sharpley. Interpolation of operators (Academic Press, 1988). Y. Brudnyi and N. Krugljak. Interpolation functors and interpolation spaces, vol. I (North- Holland, 1991). F. Cobos, M. Cwikel and P. Matos. Best possible compactness results of Lions-Peetre type. Proc. Edinburgh Math. Soc. 44 (2001), 153{172. F. Cobos, A. Manzano, A. Mart__nez and P. Matos. On interpolation of strictly singular operators, strictly cosingular operators and related operator ideals. Proc. Royal Soc. Edinb. 130A (2000), 971{989. M. Cwikel and E. Pustylnik. Weak type interpolation near `endpoint' spaces. J. Funct. Anal. 171 (2000), 235{277. A. A. Dmitriev. The interpolation of one-dimensional operators, Vorone_z Gos. Univ. Trudy Nau_cn.-Issled. Inst. Mat. VGU Vyp. 11Sb. Statej Funkcional. Anal. i Prilozen 11 (1973), 31{43 (Russian). A. García del Amo, F. L. Hernández, V. M. S_anchez and E. M. Semenov. Disjointly strictlysingular inclusions between rearrangement invariant spaces. J. London Math. Soc. 62 (2000), 239{252. S. Goldberg. Unbounded linear operators (McGraw-Hill, 1966). A. Grothendieck. Sur certains sous-espaces vectoriels de Lp. Canad. J. Math. 6 (1954), 158{ 160. F. L. Hernández and B. Rodríguez-Salinas. On `p-complemented copies in Orlicz spaces II. Israel J. Math. 68 (1989), 27{55. T. Kato. Perturbation theory for nullity, de_ciency and other quantities of linear operators. J. Analyse Math. 6 (1958), 273{322. S. G. Kre__n, Ju. I. Petunin and E. M. Semenov. Interpolation of Linear Operators. Amer. Math. Soc. (Providence, R.I., 1982). J. Lindenstrauss and L. Tzafriri. Classical Banach Spaces, vol. I, Sequence spaces (Springer, 1977). S. Ya. Novikov. Boundary spaces for inclusion map between rearrangement invariant spaces. Collect. Math. 44 (1993), 211{215. A. Pelczy_ nski. On strictly singular and strictly cosingular operators. Bull. Acad. Polon. Sci., S_er. Sci. Math. Astronom. Phys. 13 (1965), 31{36; 37{41. A. Pietsch. Operator ideals (North-Holland, 1980). E. Pustylnik. Minimal and maximal intermediate Banach spaces. Ukrainian Math. J. 29 (1977), 102{107. E. Pustylnik. On optimal interpolation and some interpolation properties of Orlicz spaces. Soviet. Math. Dokl. 27 (1983), 333{336. (Translation from Dokl. Akad. Nauk SSSR 69 (1983)). E. Pustylnik. Embedding functions and their role in interpolation theory. Abstract and Applied Analysis 1 (1996), 305{325. I. Singer. Bases in Banach spaces I (Springer, 1970). I. Singer. Bases in Banach spaces II (Springer, 1981).