Publication: Orthogonally additive holomorphic functions on open
subsets of C(K)
Loading...
Full text at PDC
Publication Date
2012
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
We introduce, study and characterize orthogonally additive holomorphic functions f:U -> a", where U is an open subset of C(K). We are led to consider orthogonal additivity at different points of U.
Description
UCM subjects
Unesco subjects
Keywords
Citation
Aron, R., Berner, P.: A Hahn-Banach extension theorem for analytic mappings. Bull. Soc. Math. France 106(1), 3–24 (1978)
Benyamini, Y., Lassalle, S., Llavona, J.G.: Homogeneous orthogonally-additive polynomials on Banach lattices. Bull. Lond. Math. Soc. 38(3), 459–469 (2006)
Carando, D., Lassalle, S., Zalduendo, I.: Orthogonally additive polynomials over C(K) are measures—a short proof. Integral Equ. Oper. Theory 56, 597–602 (2006)
Carando, D., Lassalle, S., Zalduendo, I.: Orthogonally additive holomorphic functions of bounded type over C(K). Proc. Edinb. Math. Soc. 53(2), 609–618 (2010)
Dineen, S.: Complex Analysis in Infinite Dimensional Spaces. Springer Monographs in Mathematics. Davie, A., Gamelin, T.: A theorem on polynomial-star approximation. Proc. Am. Math. Soc. 106(2), 351–356 (1989)
Mujica, J.: Complex Analysis on Banach Spaces. Dover, Mineola (2010)
Palazuelos, C., Peralta, A.M., Villanueva, I.: Orthogonally additive polynomials on C∗-algebras. Q. J. Math. 59(3), 363–374 (2008)
Pérez-García, D., Villanueva, I.: Orthogonally additive polynomials on spaces of continuous functions. J. Math. Anal. Appl. 306(1), 97–105 (2005)
Sundaresan, K.: Geometry of spaces of homogeneous polynomials on Banach lattices. In: Applied Geometry and Discrete Mathematics. DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 4, pp. 571–586. Amer. Math. Soc., Providence (1991)