TY - JOUR
ID - 4975
TI - Anti-N-order polynomial Daugavet property on Banach spaces
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Emenyu, John
AD - Department of Mathematics, Faculty of Science, Mbarara University of Science and Technology, Uganda
Y1 - 2021
PY - 2021
VL - 12
IS - 1
SP - 1097
EP - 1105
KW - Banach spaces
KW - local and uniform convexity
KW - polynomials
KW - N-order polynomial Daugavet equation
KW - anti-N-order Daugavet property
DO - 10.22075/ijnaa.2019.16371.1865
N2 - 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 normsbelong to the approximate spectra.
UR - https://ijnaa.semnan.ac.ir/article_4975.html
L1 - https://ijnaa.semnan.ac.ir/article_4975_dcbcd4a6a92b6b490dbbbb5250a63af9.pdf
ER -