Ferrera Cuesta, Juan (2002) Norm-attaining polynomials and differentiability. Studia Mathematica, 151 (1). pp. 1-21. ISSN 0039-3223
We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Frechet differentiable: We also characterize the Gateaux differentiability of the norm. Finally we study those properties for some classical Banach spaces.
|Uncontrolled Keywords:||Banach spaces; Polynomials; Norm differentiability; Shmul'yans's test; Strongly attains its norm; Fréchet differentiability; Gâteaux differentiability|
|Subjects:||Sciences > Mathematics > Mathematical analysis|
M. D. Acosta, F. Aguirre and R. Payá, There is no bilinear Bishop-Phelps theorem, Israel J. Math. 93 (1996), 221–227.
R. Alencar, R. M. Aron and S. Dineen, A reflexive space of holomorphic functions in infinitely many variables, Proc. Amer. Math. Soc. 90 (1984), 407–411.
R. M. Aron, Compact polynomials and compact differentiable mappings between Banach spaces, in: Sém. P. Lelong 1974/75, Lecture Notes in Math. 524, Springer, 1976, 213–222.
R. M. Aron and P. D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. Math. France 106 (1978), 3–24.
R. M. Aron, C. Finet and E. Werner, Some remarks on norm-attaining n -linear forms, in: Function Spaces (Edwardsville, 1994), Lecture Notes in Pure and Appl. Math. 172, Dekker, New York, 1995, 19–28.
C. Benítez, Y. Sarantopoulos and A. Tonge, Lower bounds for norms of products of polynomials, Math. Proc. Cambridge Philos. Soc. 124 (1998), 395–408.
Y. S. Choi and S. G. Kim, Polynomial properties of Banach spaces, J. Math. Anal. Appl. 190 (1995), 203–210.
Y. S. Choi, S. G. Kim, Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc. 54 (1996), 135–147.
A. M. Davie and T. W. Gamelin, A theorem on polynomial-star approximation, Proc. Amer. Math. Soc. 106 (1989), 351–356.
R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Surveys Pure Appl. Math. 64, Longman, 1993.
J. Diestel, Sequences and Series in Banach Spaces, Springer, Berlin, 1984.
S. Dineen, Complex Analysis on Infinite-Dimensional Spaces, Springer, London, 1999.
S. Dineen, A Dvoretzky theorem for polynomials, Proc. Amer. Math. Soc. 123 (1995), 2817–2821.
J. Ferrera, J. Gómez and J. G. Llavona, On completion of spaces of weakly continuous functions, Bull. London Math. Soc. 15 (1983), 260–264.
J. Gutiérrez, J. Jaramillo and J. G. Llavona, Polynomials and geometry of Banach spaces, Extracta Math. 10 (1995), 79–114.
J. Jaramillo, A. Prieto and I. Zalduendo, The bidual of the space of polynomials on a Banach space, Math. Proc. Cambridge Philos. Soc. 122 (1997), 457–471.
J. Llavona, Approximation of Continuously Differentiable Functions, North-Holland Math. Stud. 130, North-Holland, 1986.
J. Mujica, Complex Analysis in Banach Spaces, North-Holland Math. Stud. 120, North-Holland, 1986.
R. A. Ryan, Dunford-Pettis properties, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 373–379.
C. Stegall, Optimization and differentiation in Banach spaces, Linear Algebra Appl. 84 (1986), 191–211
|Deposited On:||17 May 2012 09:46|
|Last Modified:||17 May 2012 09:46|
Repository Staff Only: item control page