Weakly Sequentially Continuous Analytic Functions on a Banach Space

  1. Aron, Richard M.
  2. Herves, Carlos
Livre:
Functional Analysis, Holomorphy and Approximation Theory II

ISSN: 0304-0208

Année de publication: 1984

Pages: 23-38

Type: Chapitre d'ouvrage

DOI: 10.1016/S0304-0208(08)70820-X GOOGLE SCHOLAR lock_openAccès ouvert editor

Résumé

Let Hwsc(E) be the space of complex valued analytic functions on the complex Banach space E which map weakly convergent sequences to convergent sequences. Hwsc(E) contains, in general properly, the space Hw(E) of analytic functions on E which are weakly continuous on bounded subsets of E and is, in general, properly contained in the space Hd(E) of analytic functions which are bounded on weakly compact subsets of E. Here we study more closely the relation between these spaces. We show, for example, that for many Banach spaces E, a function f belongs to Hwsc (E) if and only if its differential df belongs to the ε-product Hd(E) ε E'.

Références bibliographiques

  • R. Alencar, R. Aron, S. Dineen, A reflexive space of holomorphic functions in infinitely many variables, to appear in Proc. A.M.S
  • Aron, (1979), Adv. in Hol. J.A. Barroso, North-Holland Math. Studies, 34, pp. 47, 10.1016/S0304-0208(08)70753-9
  • Aron, (1979)
  • R. Aron, C. Herves, M. Valdivia, Weakly continuous mappings on a Banach space, to appear in J. Funct. Anal
  • Aron, (1980), J. reine angew, Math. (Crelle), 313, pp. 195
  • Dineen, (1981), Studies, pp. 57
  • S. Dineen, Entire functions on co, to appear in J. Funct. Anal
  • Dineen, (1972), Math. Ann., 196, pp. 106, 10.1007/BF01419608
  • Ferrera, (1982), Pac. J. Math., 102, pp. 285, 10.2140/pjm.1982.102.285
  • Ferrera, (1980)
  • Ferrera, (1983), Bull. L.M.S., 15, pp. 260, 10.1112/blms/15.3.260
  • Gomes Gil, (1981)
  • Gomez GIL, (1982), Proc. Royal Irish Acad., 82A, pp. 141
  • Horvath, (1966), 1
  • James, (1950), Ann. Math., 52, pp. 518, 10.2307/1969430
  • Josefson, (1975)
  • (1978), J. Math. Pures et Appl., 57, pp. 397
  • Nachbin, (1969), 47
  • Paredes Alvarez, (1981)
  • Pelczynski, (1963), Bull. Acad. Pol. Sc., XI, pp. 379
  • Rosenthal, (1978), Bull. A.M.S., 84, pp. 803, 10.1090/S0002-9904-1978-14521-2
  • Schwartz, (1957), Ann. Inst. Fourier, 7, pp. 1, 10.5802/aif.68
  • Tsirel'Son, (1974), Funct. Anal, and Appl., 8, pp. 138, 10.1007/BF01078599
  • Valdivia, (1977), J. Funct. Anal., 24, pp. 1, 10.1016/0022-1236(77)90002-7