Abstract
Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone.
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References
R. Deville, G. Godefroy, V. Zizler, Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys 64, Longman Ed (1993).
M. Fabian, P. Habala, P. Hájek, V. Montesinos, J. Pelant, V. Zizler, Functional analysis and infinite dimensional geometry. Canadian Math. Soc. Books, Springer Verlag, (2001).
M. Fabian, V. Montesinos, V. Zizler, Smoothness in Banach spaces. Selected problems. Rev. R. Acad. Cien. Serie A Mat. 100, (2006), 101–125.
T. Figiel, On the moduli of convexity and smoothness. Studia Math. 56, (1976), 121–155.
M. Zippin, A remark on bases and reflexivity in Banach spaces. Isr. J. Math. 6, (1968), 74–79.
P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm. Isr. J. Math 13, (1972), 281–288.
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First author supported by the grants MTM2005-08379 of MECD (Spain), 00690/PI/04 of Fundación Séneca (CARM, Spain) and AP2003-4453 of MECD (Spain), Second author supported by AV0Z10190503 and A100190502.
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Guirao, A.J., Hájek, P. Schauder Bases under Uniform Renormings. Positivity 11, 627–638 (2007). https://doi.org/10.1007/s11117-007-2067-9
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DOI: https://doi.org/10.1007/s11117-007-2067-9