Anti-N-order polynomial Daugavet property on Banach spaces

	Anti-N-order polynomial Daugavet property on Banach spaces
International Journal of Nonlinear Analysis and Applications
مقاله 87، دوره 12، شماره 1، مرداد 2021، صفحه 1097-1105 اصل مقاله (382.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.16371.1865
نویسنده
John Emenyu^*
Department of Mathematics, Faculty of Science, Mbarara University of Science and Technology, Uganda
چکیده
We generalize the notion of the anti-Daugavet property (a-DP) to the anti-N-order polynomial Daugavet property (a-NPDP) for Banach spaces by identifying a good spectrum of a polynomial and prove that locally uniformly alternatively convex or smooth Banach spaces have the a-mDP for rank-1 polynomials. We then prove that locally uniformly convex Banach spaces have the a-NPDP for compact polynomials if and only if their norms are eigenvalues, and uniformly convex Banach spaces have the a-NPDP for continuous polynomials if and only if their norms belong to the approximate spectra.
کلیدواژه‌ها
Banach spaces؛ local and uniform convexity؛ polynomials؛ N-order polynomial Daugavet equation؛ anti-N-order Daugavet property
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