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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 | ||
| تاریخ دریافت: 09 آبان 1397، تاریخ بازنگری: 24 آبان 1398، تاریخ پذیرش: 01 آذر 1398 | ||
| 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 | ||
| مراجع | ||
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