Properties of modulus of monotonicity and Opial property in direct sums

• Autorzy: Joanna Markowicz , Stanisław Prus
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2017
• Tom: 71
• Numer: 2

Daty

wydano

2017

online

2017-12-18

Twórcy

autor

Joanna Markowicz

autor

Stanisław Prus

Bibliografia

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• 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.

Identyfikatory

DOI

10.17951/a.2017.71.2.69