Anti-N-order polynomial Daugavet property on Banach spaces
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJNAA-12-1_087
تاریخ نمایه سازی: 11 آذر 1401
Abstract:
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-۱ 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 normsbelong to the approximate spectra.
Keywords:
Banach spaces , local and uniform convexity , polynomials , N-order polynomial Daugavet equation , anti-N-order Daugavet property
Authors
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Department of Mathematics, Faculty of Science, Mbarara University of Science and Technology, Uganda