Properties of modulus of monotonicity and Opial property in direct sums

Joanna Markowicz, Stanisław Prus


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.


Banach lattice; modulus of monotonicity; direct sum; non-strict Opial property; Opial property

Full Text:



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.

Data publikacji: 2017-12-18 20:31:34
Data złożenia artykułu: 2017-12-17 11:10:26


  • There are currently no refbacks.

Copyright (c) 2017 Joanna Markowicz, Stanisław Prus