RT Journal Article
T1 Polynomial topologies on Banach spaces
A1 Garrido, M. Isabel
A1 Jaramillo Aguado, Jesús Ángel
A1 Llavona, José G.
AB On every real Banach space X we introduce a locally convex topology tau(p), canonically associated to the weak-polynomial topology w(P). It is proved that tau(p) is the finest locally convex topology on X which is coarser than w(P). Furthermore, the convergence of sequences is considered, and sufficient conditions on X are obtained under which the convergent sequences for w(P) and for tau(P) either coincide with the weakly convergent sequences (when X has the Dunford-Pettis property) or coincide with the norm-convergent sequences (when X has nontrivial type).
PB Elsevier Science
SN 0166-8641
YR 2005
FD 2005-06-05
LK https://hdl.handle.net/20.500.14352/49982
UL https://hdl.handle.net/20.500.14352/49982
LA eng
NO R. Alencar, R. Aron, S. Dineen, A reflexive space of holomorphic functions in infinitely many variables,Proc. Amer. Math. Soc. 90 (1984) 407–411.R. Aron, Y.S. Choi, J.G. Llavona, Estimates by polynomials, Bull. Austral. Math. Soc. 52 (1995) 475–486.R. Aron, B. Cole, T.W. Gamelin, Spectra of algebras of analytic functions on a Banach space, J. Reine Angew. Math. 415 (1991) 51–93.R. Aron, C. Hervés, M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983)189–203.R. Aron, J.B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980) 195–216.P. Biström, J.A. Jaramillo, M. Lindström, Polynomial compactness in Banach spaces, Rocky Mountain J.Math. 28 (1998) 1203–1226.R. Bonic, J. Frampton, Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966) 877–898.T. Carne, B. Cole, T. Gamelin, A uniform algebra of analytic functions on a Banach space, Trans. Amer.Math. Soc. 314 (1989) 639–659.J.M.F. Castillo, R. García, R. Gonzalo, Banach spaces in which all multilinear forms are weakly sequentially continuous, Studia Math. 136 (1999) 121–145.A.M. Davie, T.W. Gamelin, A theorem of polynomial-star approximation, Proc. Amer. Math. Soc. 106 (1989) 351–358.S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer, London, 1999.J. Farmer, W.B. Johnson, Polynomial Schur and polynomial Dunford–Pettis properties in Banach spaces,Contemp. Math. 144 (1993) 95–105.J. Ferrera, J. Gómez, J.G. Llavona, On completion of spaces of weakly continuous functions, Bull. London Math. Soc. 15 (1983) 260–264.K. Floret, Weakly Compact Sets, Lecture Notes in Math., vol. 801, Springer, Berlin, 1980.M. González, J. Gutiérrez, J.G. Llavona, Polynomial continuity on 1, Proc. Amer. Math. Soc. 125 (1997)1349–1353.R. Gonzalo, J.A. Jaramillo, Separating polynomials on Banach spaces, Extracta Math. 12 (1997) 145–164.J. Gutiérrez, J.G. Llavona, Polynomial continuous operators, Israel J. Math. 120 (1997) 179–187.P. Hájek, J.G. Llavona, P -continuity on classical Banach spaces, Proc. Amer. Math. Soc. 128 (2000) 827–830.J.A. Jaramillo, A. Prieto, Weak-polynomial convergence on a Banach space, Proc. Amer. Math. Soc. 118 (1993) 463–468.J. Lindenstraus, L. Tzafriri, Classical Banach Spaces, II, Springer, Berlin, 1979.J. Mujica, Complex Analysis in Banach Spaces, North-Holland Math. Stud., vol. 120, North-Holland, Amsterdam,1986.R. Ryan, Dunford–Pettis properties, Bull. Acad. Polon. Sci. 27 (1979) 373–379.
NO DGES (Spain)
DS Docta Complutense
RD 8 may 2024