Abstract
In 1979, P.Dodds and D.H.Fremlin published their famous result asserting that if E, F are Banach lattices such that E′ and F have order continuous norms and if U, V: E → F are linear operators such that 0 ≤ U ≤ V then the compacity of V implies the compacity of U.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aliprantis, C.D.; Burkinshaw, O.: The components of a positive operator, Math. Z. 184 (1983), 245–257.
Dodds, P.; Fremlin, D.H.: Compact operators in Banach lattices, Israel J. Math. 34 (1979), 287–320.
Fremlin, D.H.: Tensor products of Archimedean vector lattices, Amer. J. Math. 94 (1972), 777–798.
Fremlin, D.H.: Topological Riesz spaces and measure theory, The University Press, Cambridge, 1974.
Fuik, S.; John, O.; Kufner, A.: Function spaces, Academia, Prague, 1977.
Kaiton, N.J.; Saab, P.: Ideal properties of regular operators between Banach lattices, preprint.
Leinfelder, H.: A remark on a paper of L.D.Pitt, Bayreuth Math. Schr. 11(1982).
Lindenstrauss, J.; Tzafriri, L.: Classical Banach Spaces. I, Springer, 1977.
Lindenstrauss, J.; Tzafriri, L.: Classical Banach Spaces. II, Springer, 1979.
de Pagter, B.: The components of a positive operator, Indag. Math. 45 (1983), 219–241.
Peressini, A.: Ordered topological vector spaces, Harper Row, 1967.
Vuza, D.: Strongly lattice-ordered modules over functions algebras, INCREST Preprint Series in Math., Bucuresti, 62(1980).
Vuza, D.: Extension theorems for strongly lattice-ordered modules and applications to linear operators, INCREST Preprint Series in Math., Bucuresti, 100(1981).
Vuza, D.: The perfect M-tensor product of perfect Banach lattices, in Proceedings of the First Romanian-GDR Seminar, Lecture Notes in Math. 991(1983), Springer.
Vuza, D.: Modules over commutative ordered rings (Romanian), Thesis, Bucuresti, 1983.
Vuza, D.: Principal modules of linear maps and their applications, Proceedings of the Second International Conference on Operator Algebras, Ideals and their Applications in Theoretical Physics, Teubner-Texte zur Math. 67 (1984), pp. 212–219.
Vuza, D.: Ideals and bands in principal modules, INCREST Preprint Series in Math., Bucuresti, 42(1984); (to appear in Archiv. der Math.).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Basel AG
About this chapter
Cite this chapter
Vuza, D.T. (1986). Ideal Properties of Order Bounded Operators on Ordered Banach Spaces Which are not Banach Lattices. In: Douglas, R.G., Pearcy, C.M., Sz.-Nagy, B., Vasilescu, FH., Voiculescu, D., Arsene, G. (eds) Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, vol 17. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7698-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7698-8_25
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7700-8
Online ISBN: 978-3-0348-7698-8
eBook Packages: Springer Book Archive