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Domination by positive disjointly strictly singular operators
Author(s):
Julio
Flores;
Francisco
L.
Hernández
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1979-1986.
MSC (2000):
Primary 47B65, 46B42
Posted:
November 22, 2000
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Abstract:
We prove that each positive operator from a Banach lattice  to a Banach lattice  with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on  is order continuous. We prove as well that if  is dominated by a disjointly strictly singular operator, then  is disjointly strictly singular.
References:
-
- 1.
- Y. A. Abramovich, Weakly compact sets in topological K-spaces, Teor. Funkcii Funkional. Anal. i Prilozen 15 (1972), 27-35.
- 2.
- C.D. Aliprantis and O. Burkinshaw, Positive compact operators on Banach lattices, Math. Z. 174 (1980), 289-298. MR 81m:47053
- 3.
- -, On weakly compact operators on Banach lattices, Proc. Amer. Math. Soc. 83 (1981), 573-578. MR 82j:47057
- 4.
- -, Positive operators, Academic Press, 1985. MR 87h:47086
- 5.
- P.G. Dodds and D.H. Fremlin, Compact operators in Banach lattices, Israel J. of Math. 34 (1979), 287-320. MR 81g:47037
- 6.
- N. Dunford and J.T. Schwartz, Linear Operators. Part I, General Theory, Pure and applied Mathematics, vol. VII, Interscience, New York, 1958. MR 22:8302
- 7.
- 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. MR 97i:47075
- 8.
- 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. MR 92i:47038
- 9.
- F. L. Hernández and B. Rodríguez-Salinas, On
 -complemented copies in Orlicz spaces II, Israel J. of Math. 68 (1989), 27-55. MR 91c:46041 - 10.
- J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer-Verlag, 1977. MR 58:17766
- 11.
- -, Classical Banach Spaces II, Springer-Verlag, 1979. MR 81c:46001
- 12.
- P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, 1991. MR 93f:46025
- 13.
- A.W. Wickstead, Extremal structure of cones of operators, Quart. J. Math. Oxford Ser. (2) 32 (1981), 239-253. MR 82i:47069
- 14.
- -, Converses for the Dodds-Fremlin and Kalton-Saab theorems, Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. MR 96m:47067
- 15.
- A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983. MR 86b:46001
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Additional Information:
Julio
Flores
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Email:
jflores@sunam1.mat.ucm.es
Francisco
L.
Hernández
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Email:
pacoh@eucmax.sim.ucm.es
DOI:
10.1090/S0002-9939-00-05948-7
PII:
S 0002-9939(00)05948-7
Received by editor(s):
October 14, 1999
Posted:
November 22, 2000
Additional Notes:
This work was partially supported by DGES PB97-0240
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2000,
American Mathematical Society
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