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Let E, F be real Banach spaces, U subset-or-equal-to E and V subset-equal-to F non-void open subsets and C(k)(U) the algebra of real-valued k-times continuously Frechet differentiable functions on U, endowed with the compact open topology of ord[...]texto impreso
Let E be a complex Banach space and denote by H b (E) the space of all holomorphic functions f:E?C of bounded type, that is, bounded on bounded sets. It is known that f?H b (E) admits a factorization of the form f=g?S , with S a compact li[...]texto impreso
A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. Every compact (linear) operator is polynomially continuous. We prove that every[...]texto impreso
Gutiérrez, Joaquín M. ; Jaramillo Aguado, Jesús Ángel ; Llavona, José G. | Universidad de Extremadura, Departamento de Matemáticas | 1995In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces.
