The polynomial cluster value problem for Banach spaces

• Isidro H. Munive Lima ^[1] ; Sofía Ortega Castillo ^[1]
  1. [1] Universidad de Guadalajara

     Universidad de Guadalajara

     México

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 40, Nº 2, 2025, págs. 159-172
• Idioma: inglés
• DOI: 10.17398/2605-5686.40.2.159
• Enlaces
  • Texto completo
• Resumen

  • We reduce the polynomial cluster value problem for the algebra of bounded analytic functions, H ∞ , on the ball of Banach spaces X to the same polynomial cluster value problem for H ∞ but on the ball of those spaces which are `1 -sums of finite dimensional spaces.

• Referencias bibliográficas
  • [1] R.M. Aron, P.D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. Math. France 106 (1978), 3 – 24.
  • [2] R.M. Aron, B.J. Cole, T.W. Gamelin, Spectra of algebras of analytic functions on a Banach space, J. Reine Angew. Math. 415 (1991), 51...
  • [3] D. Carando, D. Galicer, S. Muro, P. Sevilla-Peris, Corrigendum to “Cluster values for algebras of analytic functions” [Adv. Math. 329...
  • [4] Y.S. Choi, D. Garcia, S.G. Kim, M. Maestre, Composition, numerical range and Aron-Berner extension, Math. Scand. 103 (1) (2008), 97 –...
  • [5] G.T. Cargo, The boundary behavior of Blaschke products, J. Math. Anal. Appl. 5 (1962), 1 – 16.
  • [6] P. Colwell, On the boundary behavior of Blaschke products in the unit disk, Proc. Amer. Math. Soc. 17 (1966), 582 – 587.
  • [7] A.M. Davie, T.W. Gamelin, A theorem on polynomial-star approximation, Proc. Amer. Math. Soc. 106 (2) (1989), 351 – 356.
  • [8] T.W. Gamelin, Analytic functions on Banach spaces, in “Complex potential theory (Montreal, PQ, 1993)”, NATO Adv. Sci. Inst. Ser. C: Math....
  • [9] W.B. Johnson, S. Ortega Castillo, The cluster value problem for Banach spaces, Illinois J. Math. 58 (2) (2014), 405 – 412.
  • [10] W.B. Johnson, S. Ortega Castillo, The cluster value problem in spaces of continuous functions, Proc. Amer. Math. Soc. 143 (4) (2015),...
  • [11] G. McDonald, The maximal ideal space of H ∞ + C on the ball in Cn , Canadian J. Math. 31 (1) (1979), 79 – 86.
  • [12] J. Mujica, “Complex Analysis in Banach Spaces” North-Holland Math. Stud., 120, Notas Mat., (107), North-Holland Publishing Co., Amsterdam,...
  • [13] S. Ortega Castillo, Strong pseudoconvexity in Banach spaces, Complex Anal. Synerg. 10 (2024), Paper No. 17, 16 pp.
  • [14] S. Ortega Castillo, A. Prieto, The polynomial cluster value problem, J. Math. Anal. Appl. 461 (2018), 1459 – 1470.
  • [15] F. Riesz, Über die Randwerte einer analytischen Funktion, Math. Z. 18 (1923), 87 – 95.