Jiménez Sevilla, María del Mar and Sánchez González, Luis (2010) LFC bumps on separable Banach spaces. Journal of Mathematical Analysis and Applications, 365, No. 1, 315-319 2010 (1). pp. 315-319. ISSN 0022-247X
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Official URL: http://www.sciencedirect.com/science/journal/0022247X
Abstract
In this note we construct a C∞-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Smooth bump functions; Locally depending on finitely many coordinates; Polyhedral banach spaces |
| Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |
| ID Code: | 13816 |
| References: | [1] R. Bonic and J. Frampton, Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966), 877-898. [2] M. Fabian, P. Habala, P. Hájek, V.M. Santalucía, J. Pelant and V. Zizler, Functional Analysis and Infinite-Dimensional Geometry, CMS Books in Math. vol. 8, Springer-Verlag, New York, (2001). [3] M. Fabian and V. Zizler, A note on bump functions that locally depend on finitely many coordinates, Bull. Austral. Math. Soc 56 (3) (1997), 447-451. [4] V. P. Fonf, Polyhedral Banach spaces, Math. Notes Acad. Sci. USSR 30 (1981), 809-813. [5] V. P. Fonf, Three characterizations of polyhedral Banach spaces, Ukrainian Math. J. 42 (9) (1990), 1145-1148. [6] P. Hájek, Smooth norms that depend locally on finitely many coordinates, Proc. Amer. Math. Soc. 123 (12) (1995), 3817-3821. [7] P. Hájek and V. Zizler, Functions locally dependent on finitely many coordinates, R. Acad. Cien. Serie A. Mat. 100 (1-2) (2006), 147-154. [8] P. Hájek and M. Johanis, Smoothing of bump functions, J. Math. Anal. Appl. 338 (2008), 1131-1139. [9] P. Hájek and M. Johanis, Polyhedrality in Orlicz Spaces, Israel J. Math. 168 (2008), 167-188. [10] R. G. Haydon, Smooth functions and partitions of unity on certains Banach spaces, Quart. J. Math. Oxford. Ser. 47 (188) (1996), 455-468. [11] M. Johanis, Locally at Banach spaces, Czechoslovak Math. J. 59 (134) (2009), no. 1, 273{284. [12] W. B. Johnson and J. Lindenstrauss, Handbook of the Geometry of Banach Spaces, vol. 1, Elsevier, 2001. [13] V. L. Klee, Polyhedral sections of convex bodies, Acta. Math. 103 (1969), 243-267. [14] D. H. Leung, Some isomorphically polyhedral Orlicz sequence spaces, Israel J. Math. 87 (1994), 117-128. [15] J. Pechanec, J. H. M. Whitfield and V. Zizler, Norms locally dependent on finitely many coordinates, An. Acad. Brasil. Ciênc. 53 (3) (1981), 415-417. [16] H. Torunczyk, Smooth partitions of unity on some nonseparable Banach spaces, Studia Math. 46 (1973), 43-51. |
| Deposited On: | 10 Nov 2011 13:32 |
| Last Modified: | 10 Nov 2011 14:13 |
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