A geometric proof of a theorem about non-dual renormings
HTML articles powered by AMS MathViewer
- by Libor Veselý PDF
- Proc. Amer. Math. Soc. 127 (1999), 2807-2809 Request permission
Abstract:
We give a simple geometric proof of a result by Davis and Johnson that every nonreflexive Banach space $X$ admits an equivalent norm in which $X$ is not isometric to a dual space. Moreover, our renorming keeps unchanged the original norm on a given finite-codimensional subspace and makes this subspace norm-one complemented.References
- William J. Davis and William B. Johnson, A renorming of nonreflexive Banach spaces, Proc. Amer. Math. Soc. 37 (1973), 486–488. MR 310595, DOI 10.1090/S0002-9939-1973-0310595-8
- Dick van Dulst and Ivan Singer, On Kadec-Klee norms on Banach spaces, Studia Math. 54 (1975/76), no. 3, 205–211. MR 394132, DOI 10.4064/sm-54-3-205-211
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Richard B. Holmes, A course on optimization and best approximation, Lecture Notes in Mathematics, Vol. 257, Springer-Verlag, Berlin-New York, 1972. MR 0420367, DOI 10.1007/BFb0059450
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- S. V. Konyagin, A remark on renormings of nonreflexive spaces and the existence of a Chebyshev center, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2 (1988), 81–82 (Russian); English transl., Moscow Univ. Math. Bull. 43 (1988), no. 2, 55–56. MR 938075
- Helmut H. Schaefer, Topological vector spaces, Graduate Texts in Mathematics, Vol. 3, Springer-Verlag, New York-Berlin, 1971. Third printing corrected. MR 0342978, DOI 10.1007/978-1-4684-9928-5
Additional Information
- Libor Veselý
- Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
- Email: libor@vmimat.mat.unimi.it
- Received by editor(s): September 22, 1998
- Received by editor(s) in revised form: November 30, 1998
- Published electronically: May 19, 1999
- Communicated by: Dale Alspach
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2807-2809
- MSC (1991): Primary 46B03; Secondary 46B10
- DOI: https://doi.org/10.1090/S0002-9939-99-05395-2
- MathSciNet review: 1670431