Flores Álvarez, Julio and Hernández, Francisco L. (2001) Domination by positive disjointly strictly singular operators. Proceedings of the American Mathematical Society, 129 (7). pp. 1979-1986. ISSN 0002-9939
Restricted to Repository staff only until 31 December 2020.
We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E --> E is dominated by a disjointly strictly singular operator, then S-2 is disjointly strictly singular.
|Uncontrolled Keywords:||Compact operators; Banach lattices|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
Y. A. Abramovich, Weakly compact sets in topological K-spaces, Teor. Funkcii Funkional. Anal. i Prilozen 15 (1972), 27-35.
C.D. Aliprantis and O. Burkinshaw, Positive compact operators on Banach lattices, Math. Z. 174 (1980), 289-298.
On weakly compact operators on Banach lattices, Proc. Amer. Math. Soc. 83 (1981), 573-578.
Positive operators, Academic Press, 1985.
P.G. Dodds and D.H. Fremlin, Compact operators in Banach lattices, Israel J. of Math. 34 (1979), 287-320.
N. Dunford and J.T. Schwartz, Linear Operators. Part I, General Theory, Pure and applied Mathematics, vol. VII, Interscience, New York, 1958.
A. García Del Amo, F. L. Hernández, and C. Ruiz, Disjointly strictly singular operators and interpolation, Proc. Royal Soc. of Edinburgh 126A (1996), 1011-1026.
F. L. Hernández, Disjointly Strictly-Singular Operators in Banach Lattices, Proc. 18 Winter School on Abstract Analysis (Srni). Acta Universitatis Carolinae-Mathematica et Physica 31(1990), 35-40.
F. L. Hernández and B. Rodríguez-Salinas, On lp-complemented copies in Orlicz spaces II, Israel J. of Math. 68 (1989), 27-55.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer-Verlag, 1977.
Classical Banach Spaces II, Springer-Verlag, 1979.
P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, 1991.
A.W. Wickstead, Extremal structure of cones of operators, Quart. J. Math. Oxford Ser. (2) 32 (1981), 239-253.
Converses for the Dodds-Fremlin and Kalton-Saab theorems, Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179.
A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983.
|Deposited On:||24 Jul 2012 11:56|
|Last Modified:||08 Nov 2013 18:45|
Repository Staff Only: item control page