Disjointly strictly singular operators and interpolation

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Cambridge University Press
Google Scholar
Research Projects
Organizational Units
Journal Issue
Interpolation properties of the class of disjointly strictly singular operators on Banach lattices are studied. We also give some applications to compare the lattice structure of two rearrangement invariant function spaces. In particular, we obtain suitable analytic characterisations of when the inclusion map between two Orlicz function spaces is disjointly strictly singular.
Unesco subjects
C. Bennett and R. Sharpley. Interpolation of operators (New York: Academic Press, 1988). J. Bergh and J. Lofstrom. Interpolation spaces. An introduction (Berlin: Springer, 1976). O. J. Beucher. On interpolation of strictly (co-) singular linear operators. Proc. Roy. Soc. Edinburgh Sect. A 112(1989), 263-9. F. Cobos, T. Kiihn and T. Schonbek. One-sided compactness results for Aronszajn-Gagliardo functors. J. Funct. Anal. 106 (1992), 274-313. S. J. Dilworth. A scale of linear spaces related to the Lp scale. Illinois J. Math. 34 (1990), 140-58. A. García del Amo. Clases de operadores singulares en reticulos de Banach. Desigualdades con pesos y funciones maximales (Ph.D. Thesis, Universidad Complutense de Madrid, 1993). A. García del Amo and F. L. Hernández. On embeddings of function spaces into If +13. Contemp. Math. 144(1993), 107-13. J. Gustavsson and J. Peetre. Interpolation of Orlicz spaces. Studia Math. 60 (1977), 33-59. S. Heinrich. Closed operator ideals and interpolation. J. Funct. Anal. 35 (1980), 397-411. F. L. Hernández. Disjointly strictly-singular operators in Banach lattices. 18th Winter School on Abstract Analysis (Srni, 1990). Acta Univ. Carolin.-Math. Phys. 31 (1990), 35-40. F. L. Hernández and B. Rodríguez-Salinas. On lp-complemented copies in Orlicz spaces II. Israel J. Math. 68 (1989), 27-55. F. L. Hernández and B. Rodríguez-Salinas. Orlicz spaces containing singular lp-complemented copies. Function spaces Conference (Poznan, 1989). Teubner-Texte Math. 120 (1991), 15-22. F. L. Hernández and C. Ruiz. Universal classes of Orlicz function spaces. Pacific J. Math. 155 (1992), 87-98. H. Hudzik. Notes on Orlicz spaces. Function spaces Conference (Poznan, 1989). Teubner-Texte Math. 120(1989), 23-9. N. J. Kalton. Orlicz sequence spaces without local convexity. Math. Proc. Cambridge Philos. Soc. 81 (1977), 253-77. J. Lindenstrauss and L. Tzafriri. Classical Banach spaces, Vol. II (Berlin: Springer, 1979). N. J. Nielsen. On the Orlicz function spaces LM(0, oo). Israel J. Math. 20 (1975), 237-59. S. Ya. Novikov. Boundary spaces for inclusion map between rearrangement invariant spaces. Function spaces (Poznan, 1992). Collect. Math. 44 (1993), 211-15. S. Ya. Novikov, E. M. Semenov and E. V. Tokarev. The structure of subspaces of the space Ap(p). Soviet Math. Dokl. 20 (1979), 760-1. L. E. Persson. Interpolation with a parameter function. Math. Scand. 59 (1986), 199-222. A. Pietsch. Operator ideals (Amsterdam: North-Holland, 1980). N. Popa. Uniqueness of the symmetric structure in Lp(fi) for 0 < p < 1. Rev. Roumaine Math. Pures Appl. 27(1982), 1061-89. N. Popa. Interpolation theorems for rearrangement invariant p-spaces of functions, 0 < p < 1, and some applications. 10th Winter School on Abstract Analysis (Srni, 1982). Rend. Circ. Mat. Palermo (2) 1982, Suppl. 2 (1982), 199-216. C. Ruiz. Estructura de espacios de Orlicz de funciones y de sucesiones con pesos. Subespacios distinguidos (Ph.D. Thesis, Universidad Complutense de Madrid, 1990). H. H. Schaefer. Banach lattices and positive operators (Berlin: Springer, 1974).