پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 713 |
| تعداد مقالات | 10,263 |
| تعداد مشاهده مقاله | 72,057,791 |
| تعداد دریافت فایل اصل مقاله | 63,817,701 |
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 | ||
|
[1] Y.A. Abramovich, A generalization of a theorem of J. Holub, Proc. Amer. Math. Soc. 108 (1990) 937–939. [2] Y.A. Abramovich, C.D. Aliprantis and O. Burkinshaw, The Daugavet equation in uniformly convex Banach spaces, J. Funct. Anal. 97 (1991) 215–230. [3] J. Appell, E. De Pascale and A. Vignoli, Nonlinear Spectral Theory, de Gruyter series in nonlinear analysis and applications 10, de Gryter-Verlag, Berlin. New York, 2004. [4] R. Aron, C. Herves and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983) 189–204. [5] R.M. Aron and J.B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980) 195–216. [6] R.M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Anal. 21 (1976) 7–30. [7] V.F. Babenko and S.A. Pichugov, On a property of compact operators in the space of integrable functions, Ukrainian Math. J. 33 (1981) 374–376. [8] B. Beauzamy, Introduction to Banach spaces and their geometry, North-Holland, Amsterdam-New York-Oxford, 2nd ed., 1985. [9] S. Burysek, On the spectra of nonlinear operators, Comment. Math. Univ. Carolin. 11 (1970) 727–743. [10] P. Chauveheid, On a property of compact operators in Banach spaces, Bull. Soc. Roy. Sci. Li´ege, 51 (1982) 371–376. [11] Y.S. Choi, D. Garcıa, M. Maestre and M. Martın, The Daugavet equation for polynomials, Studia Math. 178 (2007) 63–82. [12] Y.S. Choi, D. Garcıa, M. Maestre and M. Martın, The polynomial numerical index for some complex vector-valued function spaces, Quart. J. Math. 59 (2008) 455–474. [13] I.K. Daugavet, On a property of completely continuous operators in the space C. Uspekhi Mat. Nauk, 18.5 (1963) 157–158 (Russian). [14] J. Diestel, Geometry of Banach spaces: Selected topics, Lecture Notes in Math., 485. Springer, Berlin-Heidelberg, New York, 1975. [15] S. Dineen, Complex analysis on infinite-dimensional spaces, Springer-Verlag, London, 1990. [16] J. Emenyu, An invariant subspace problem for multilinear operators on Banach spaces and algebras, J. Ineq. Appl. 2016 (2016). [17] J. Emenyu, An invariant subspace problem for multilinear operators on finite-dimensional spaces, Nonlinear Anal. TMA 43 (2014) 1–10. [18] C. Foias and I. Singer, Points of diffusion of linear operators and almost diffuse operators in spaces of continuous functions, Math. Z. 87 (1965) 434–450. [19] J.D. Hardtke, Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness, Banach J. Math. Anal. 8 (2014) 295–334. [20] J.R. Holub, A property of weakly compact operators on C[0, 1], Proc. Amer. Math. Soc. 97 (1986) 396–398. [21] J.R. Holub, Daugavet’s equation and operators on L1(µ), Proc. Amer. Math. Soc. 100 (1987) 295–300. [22] V.M. Kadets, Some remarks concerning the Daugavet equation, Quaest. Math. 19 (1996) 225–235. [23] V.M. Kadets, R.V. Shvidkoy, G.G. Sirotkin, and D. Werner, Banach spaces with the Daugavet property, Trans. Amer. Math. Soc. 352 (2000) 855–873. [24] H. Kamowitz, A property of compact operators, Proc. Amer. Math. Soc. 91 (1984) 231–236. [25] C.-S. Lin, Generalized Daugavet equations and invertible operators on uniformly convex Banach spaces, J. Math. Anal. Appl. 197 (1996) 518–528. [26] G.Ya. Lozanovskii, On almost integral operators in KB-spaces, Vestnik Leningrad Univ. Mat. Mekh. Astr. 21(7) (1966) 35–44 (Russian). [27] M. Martın, J. Merı, and M. Popov, The polynomial Daugavet property for atomless L1(µ)-spaces, Arch. Math. 94 (2010) 383–389. [28] J. Mujica, Complex Analysis in Banach Spaces, Math. Stud., 120, North-Holland, 1986. [29] P. Santucci and M. Vath, On the definition of eigenvalues for nonlinear operators, Nonlinear Anal. 40 (2000) 565–576. [30] K. D. Schmidt, Daugavet’s equation and orthomorphisms, Proc. Amer. Math. Soc. 108 (1990) 905–911. [31] M. Vath, The Furi-Martelli-Vignoli spectrum vs. the phantom, Nonlin. Anal. TMA 47 (2001) 2237–2248. [32] P. Wojtaszczyk, Some remarks on the Daugavet equation, Proc. Amer. Math. Soc. 115 (1992) 1047–1052. | ||
|
آمار تعداد مشاهده مقاله: 15,936 تعداد دریافت فایل اصل مقاله: 9,514 |
||