Publication: P-continuity on classical Banach spaces
Full text at PDC
Advisors (or tutors)
American Mathematical Society
Given a Banach space X and an integer n, the existence of an n-homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on B-X is investigated. We provide a complete characterization for some classical Banach spaces, while for others a surprising unresolved difficulty is encountered for a certain value of n (depending on X).
R. M. Aron, Y. S. Choi and J. G. Llavona, Estimates by Polynomials, Bull. Austral. Math. Soc. 52 (1995), 475–486. J. Diestel, Sequences and series in Banach spaces, Grad. Texts in Math. 92, Springer, Berlin, 1984. J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, 1996. M. González, J. M. Gutiérrez and J. G. Llavona, Polynomial continuity on1, Proc. Amer. Math. Soc. 125, no. 5 (1997), 1349–1353. J. M. Gutiérrez and J. G. Llavona, Polynomially continuous operators, Israel J. Math. 102 (1997), 179–183.