LOCAL AND UNIFORM NEAR SMOOTHNESS OF SOME BANACH SPACES
Main Article Content
Abstract
In this paper we give an estimate of the modulus of near smoothness of the space $c_o(E_i)$. In the case of the space $c_o(l_{p_i})$ the exact formula for this modulus is derived. Moreover, we show that the properties of near uniform smoothness and local near uniform smoothness are hereditary with respect to the product space $c_o(E_i)$.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
J. Banas and K . Fraczek, "Conditions involving compactness in geometry of Banach spaces," Nonlinear Analysis, 20(1993), 1217-1230.
J. Banas and K . Fraczek, "Locally nearly uniformly smooth Banach spaces," Collect. Math., 44(1993), 13-22.
J. Banas, "Compacness conditions in geometric theory of Banach spaces," Nonlin. Anal., T.M.A., 16(1991), 669-682.
J. Banas and K. Sadarangani, "Near smoothness of Banach spaces," Collect. Math., 46(1995), 279-287.
J. Banas and K. Goebel, "Measures of noncompacness in Banach spaces," Lecture Notes in Pure and Applied Mathematics, 60(1980), Marcel Dekker, New York.
I. E. Leonard, "Banach sequences spaces," J. Math. Analysis Aplic., 54(1976), 245-265
L. Olszowy, "The modulus of near smoothness of the [P product _of a sequences of Banach spaces," Glasgow Math. J., 39(1997), 153-165.
J. R. Partington, "On nearly uniformly convex Banach spaces," Math. Proc. Comb. Phil. Soc., 93(1983), 127-129.
S. Prus, "Nearly uniformly smooth Banach spaces," Boll. Un. Math. Ital. (7), 3-B(1989), 507-512.
S. Prus, "On the modulus of noncompact convexity in a Banach space," Arch. Math. (Basel), 63(1994), 441-448.