González LLavona, José Luis and Gutiérrez, Joaquín M. (1997) Polynomially continuous operators. Israel Journal of Mathematics , 102 . 179-187 . ISSN 0021-2172
Restricted to Repository staff only until 31 December 2020.
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 polynomially continuous operator is weakly compact.
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
R. Alencar, R. M. Aron and S. Dineen, A reflexive space of holomorphic functions in infinitely many variables, Proceedings of the American Mathematical Society 90 (1984), 407–411.
R. M. Aron, Y. S. Choi and J. G. Llavona, Estimates by polynomials, Bulletin of the Australian Mathematical Society 52 (1995), 475–486.
R. M. Aron, M. Lacruz, R. A. Ryan and A. M. Tonge, The generalized Rademacher functions, Note di Matematica 12 (1992), 15–25.
R. M. Aron and J. B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, Journal für die reine und angewandte Mathematik 313 (1980), 195–216.
T. K. Carne, B. Cole and T. W. Gamelin, A uniform algebra of analytic functions on a Banach space, Transactions of the American Mathematical Society 314 (1989), 639–659.
H. S. Collins, Completeness and compactness in linear topological spaces, Transactions of the American Mathematical Society 79 (1955), 256–280.
L. A. Harris, Bounds on the derivatives of holomorphic functions of vectors, in Colloque d'Analyse (L. Nachbin, ed.), Rio de Janeiro, 1972, pp. 145–163.
T. Jech, Set Theory, Monographs and Textbooks in Pure and Applied Mathematics 79, Academic Press, New York, 1978.
M. Lacruz, Four Aspects of Modern Analysis, Ph.D. Thesis, Kent State University, Kent, OH, 1991.
J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in L p -spaces and their applications, Studia Mathematica 29 (1968), 275–326.
J. Mujica, Complex Analysis in Banach Spaces, Math. Studies 120, North-Holland, Amsterdam, 1986.
R. A. Ryan, Holomorphic mappings on ℓ 1 , Transactions of the American Mathematical Society 302 (1987), 797–811.
|Deposited On:||10 Sep 2012 10:04|
|Last Modified:||10 Sep 2012 10:04|
Repository Staff Only: item control page