ArticleOriginal scientific text
Title
Properties of modulus of monotonicity and Opial property in direct sums
Authors ,
Abstract
We give an example of a Banach lattice with a non-convex modulus of monotonicity, which disproves a claim made in the literature. Results on preservation of the non-strict Opial property and Opial property under passing to general direct sums of Banach spaces are established.
Keywords
Banach lattice, modulus of monotonicity, direct sum, non-strict Opial property, Opial property
Bibliography
- Day, M. M., Normed Linear Spaces, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1962.
- Hardtke, J.-D., WORTH property, Garcıa-Falset coefficient and Opial property of infinite sums, Comment. Math. 55 (2015), 23-44.
- Kirk, W. A., Sims, B. (eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publ., Dordrecht, 2001.
- Kutzarova, D., Landes, T., Nearly uniform convexity of infinite direct sums, Indiana Univ. Math. J. 41, No. 4 (1992), 915-926.
- Kurc, W., A dual property to uniform monotonicity in Banach lattices, Collect. Math. 44 (1993), 155-165.
- Lindenstrauss, J., Tzafriri, L., Classical Banach Spaces II, Springer-Verlag, New York, 1979.
- Meyer-Nieberg, P., Banach Lattices, Springer-Verlag, Berlin, 1991.
- Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
Main language of publication
English
Published
2017
Published online
2017-12-18
Exact and natural sciences