Jiménez Sevilla, M.; Moreno, J. P. On denseness of certain norms in Banach spaces. (English) Zbl 0866.46007 Bull. Aust. Math. Soc. 54, No. 2, 183-196 (1996). Summary: We give several results dealing with denseness of certain classes of norms with many vertex points. We prove that, in Banach spaces with the Mazur or the weak* Mazur intersection property, every ball (convex body) can be uniformly approximated by balls (convex bodies) being the closed convex hull of their strongly vertex points. We also prove hat given a countable set \(F\), every norm can be uniformly approximated by norms which are locally linear at each point of \(F\). Cited in 1 Document MSC: 46B20 Geometry and structure of normed linear spaces Keywords:convex body; weak* Mazur intersection property; ball; strongly vertex points PDFBibTeX XMLCite \textit{M. Jiménez Sevilla} and \textit{J. P. Moreno}, Bull. Aust. Math. Soc. 54, No. 2, 183--196 (1996; Zbl 0866.46007) Full Text: DOI References: [1] Georgiev, C.R. Acad. Bulgare. Sci. 43 pp 13– (1990) [2] Georgiev, Math. Balkanica 5 pp 20– (1991) [3] DOI: 10.1112/plms/s3-51.1.113 · Zbl 0549.46025 · doi:10.1112/plms/s3-51.1.113 [4] Deville, Smoothness and renormings in Banach spaces 64 (1993) · Zbl 0782.46019 [5] DOI: 10.1007/BF01190117 · Zbl 0815.46013 · doi:10.1007/BF01190117 [6] DOI: 10.1007/BF02764721 · Zbl 0589.03012 · doi:10.1007/BF02764721 [7] DOI: 10.1007/BF02760971 · Zbl 0542.46013 · doi:10.1007/BF02760971 [8] Moreno, Bull. Sci. Math. [9] Moreno, Rocky Mountain J. Math [10] Mazur, Studia Math. 4 pp 128– (1933) [11] Sevilla, J. Funct. Anal [12] Kunen, Handbook of set theoretic topology (1984) · Zbl 0546.00022 [13] Sevilla, C.R. Acad. Sci. Paris Séric. I Math. 321 pp 1219– (1995) [14] Godun, Contemp. Math. 144 pp 119– (1993) · doi:10.1090/conm/144/1209453 [15] Giles, Bull. Austral. Math. Soc. 18 pp 471– (1978) [16] DOI: 10.1007/BF01056615 · Zbl 0728.46018 · doi:10.1007/BF01056615 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.