Artículos de revistas
A Monomial Basis For The Holomorphic Functions On C0
Registro en:
Proceedings Of The American Mathematical Society. , v. 141, n. 5, p. 1663 - 1672, 2013.
29939
10.1090/S0002-9939-2012-11436-4
2-s2.0-84874198981
Autor
Dineen S.
Mujica J.
Institución
Resumen
For over thirty years it has been known that the monomials form a basis for the n-homogeneous polynomials on certain infinite dimensional Banach spaces. Recently, Defant and Kalton have shown that these are never unconditional. In this article we show that the monomials form a basis for both the holomorphic functions and the holomorphic functions of bounded type on c0, both with their natural topologies. © 2012 American Mathematical Society. 141 5 1663 1672 Alencar, R., On reflexivity and basis for P(mE) (1985) Proc. Royal Irish Acad., Sect A, 85 (2), pp. 131-138. , MR845536 (87i:46101) Defant, A., Kalton, N., Unconditionality in spaces of m-homogeneous polynomials (2005) Q.J. Math, 56, pp. 53-64. , MR2124579 (2005k:46107) Diestel, J., (1984) Sequences and Series in Banach Spaces, , Springer-Verlag, New York, MR737004 (85i:46020) Dimant, V., Dineen, S., Banach subspaces of spaces of holomorphic mappings and related topics (1998) Math. Scand, 83, pp. 142-160. , MR1662092 (99m:46031) Dineen, S., (1981) Complex Analysis in Locally Convex Spaces, , North-Holland Math. Stud., 57, MR640093 (84b:46050) Dineen, S., (1999) Complex Analysis on Infinite Dimensional Spaces, , Springer-Verlag Monographs in Mathematics, MR1705327 (2001a:46043) Galindo, P., Maestre, M., Rueda, P., Biduality in spaces of holomorphic functions (2000) Math. Scand, 86 (1), pp. 5-16. , MR1738512 (2001i:46062) Grecu, B.C., Ryan, R.A., Polynomials on Banach spaces with unconditional bases (2005) Proc. Amer. Math. Soc, 133 (4), pp. 1083-1091. , MR2117209 (2005i:46051) Jarchow, H., (1981) Locally Convex Spaces, , B.G. Teubner, Stuttgart, MR632257 (83h:46008) Matos, M., On holomorphy in Banach spaces and absolute convergence of Fourier series (1988) Port. Math, 45 (4), pp. 429-450. , and 47, 1, 1990, 13. MR982911 (90f:46075) MR1079501 (91j:46054) Mujica, J., (1986) Complex Analysis in Banach Spaces, , North-Holland Math. Studies, 120, reprinted by Dover, Mineola, New York, 2010. MR842435 (88d:46084) Ryan, R.A., Holomorphic mappings on l1 (1987) Trans. Amer. Math. Soc, 302, pp. 797-811. , MR0891648 (88h:46089) Ryan, R.A., (1980) Applications of topological tensor products to infinite dimensional holomorphy, , Thesis, Trinity College Dublin Venkova, M., Global Schauder decompositions of locally convex spaces (2007) Math. Scand, 101 (1), pp. 65-82. , MR2353242 (2008k:46005)