Properties of modulus of monotonicity and Opial property in direct sums
Joanna Markowicz; Stanisław Prus
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2017)
- Volume: 71, Issue: 2
- ISSN: 0365-1029
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Abstract
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topJoanna Markowicz, and Stanisław Prus. "Properties of modulus of monotonicity and Opial property in direct sums." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 71.2 (2017): null. <http://eudml.org/doc/289726>.
@article{JoannaMarkowicz2017,
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.},
author = {Joanna Markowicz, Stanisław Prus},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Banach lattice; modulus of monotonicity; direct sum; non-strict Opial property; Opial property},
language = {eng},
number = {2},
pages = {null},
title = {Properties of modulus of monotonicity and Opial property in direct sums},
url = {http://eudml.org/doc/289726},
volume = {71},
year = {2017},
}
TY - JOUR
AU - Joanna Markowicz
AU - Stanisław Prus
TI - Properties of modulus of monotonicity and Opial property in direct sums
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2017
VL - 71
IS - 2
SP - null
AB - 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.
LA - eng
KW - Banach lattice; modulus of monotonicity; direct sum; non-strict Opial property; Opial property
UR - http://eudml.org/doc/289726
ER -
References
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- 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.
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