Kutzarova, D. N.; Nikolova, L. Y.; Zachariades, T. Real interpolation for families of Banach spaces and convexity. (English) Zbl 0824.46023 Math. Nachr. 171, 259-268 (1995). Summary: We show how the geometrical properties of uniform convexity and uniformly non-\(\ell^ 1_ k\) are inherited by real interpolation for infinite families. Cited in 1 ReviewCited in 1 Document MSC: 46B20 Geometry and structure of normed linear spaces 46M35 Abstract interpolation of topological vector spaces 46B70 Interpolation between normed linear spaces Keywords:uniform convexity; uniformly non-\(\ell^ 1_ k\); real interpolation for infinite families PDFBibTeX XMLCite \textit{D. N. Kutzarova} et al., Math. Nachr. 171, 259--268 (1995; Zbl 0824.46023) Full Text: DOI References: [1] Properties Geometriques des Espaccs d’Interpolation, Seminaire Maurey-Schwartz, Expose 14. Ecole Polytechnique, Paris. 1974/75 [2] Espaces d’Interpolation Reels: Topologie et Geometric. Lect. Notes in Math. 666, Berlin –Heidelberg, New York, Springer Verlag 1978 · doi:10.1007/BFb0068827 [3] Beck, Proc. Amer. Math. Soc. 13 pp 329– (1962) [4] Carro, Studia Mathem. [5] Casini, Mathematica Pannonica 3/1 pp 117– (1992) [6] Coifman, Adv. in Math. 43 pp 203– (1982) [7] Cwikee, Proc. Amer. Math. Soc. 84 pp 555– (1982) [8] Day, Bull. Amer. Math. Soc. 47 pp 504– (1941) [9] Giesy, Studia Mathematica pp 61– (1973) [10] James, Ann. of Math. 80 pp 542– (1964) [11] , Classical Banach Spaces I, Sequence Spaces, Springer-Verlag Berlin–Heidelberg–New York 1977 · Zbl 0362.46013 · doi:10.1007/978-3-642-66557-8 [12] , Classical Banach Spaces II, Function Spaces, Springer-Verlag Berlin-Heidelberg-New York, 1979 · Zbl 0403.46022 · doi:10.1007/978-3-662-35347-9 [13] Mastylo, Bull. Soc. Math. Belg. 45 pp 99– (1993) [14] Nikolova, Math. Scand. 72 pp 47– (1993) · Zbl 0789.46062 · doi:10.7146/math.scand.a-12436 [15] Vignati, Proc. Amer. Math. Soc. 99 pp 4– (1987) [16] Yoshikawa, J. Fac. Sci. Univ. Tokyo 16 pp 407– (1970) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.