Complutense University Library

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


Cobos, Fernando and Pustylnik, E. (2002) On Strictly Singular and Strictly Cosingular Embeddings Between Banach Lattices of Functions. Mathematical Proceedings of the Cambridge Philosophical Society, 133 (Part 1). pp. 183-190. ISSN 0305-0041

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


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.

Item Type:Article
Uncontrolled Keywords:Spaces; Interpolation; Inclusions; Mathematics
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15145

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).

Deposited On:09 May 2012 10:53
Last Modified:06 Feb 2014 10:17

Repository Staff Only: item control page