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1 results

  • 20 - Monomial Convergence in Banach Sequence Spaces

  • from Part 3 - Replacing Polydiscs by Other Balls
  • Andreas Defant, Carl V. Ossietzky Universität Oldenburg, Germany, Domingo García, Universitat de València, Spain, Manuel Maestre, Universitat de València, Spain, Pablo Sevilla-Peris
  • Book:
    Dirichlet Series and Holomorphic Functions in High Dimensions
    Published online:
    19 July 2019
    Print publication:
    08 August 2019, pp 506-530

  • Summary

    The set of monomial convergence of the bounded holomophic functions on B_{c0} and of m-homogeneous polynomials on c0 was studied in Chapter 10. Here the space c0 is replaced by some other l_p spaces, or even by polynomials on an arbitrary Banach sequence space and holomorphic functions on Reinhardt domains. The only complete case is p=1, where the set of monomial convergence of the m-homogeneous polynomials is exactly l_1, and the set of monomial convergence of the bounded holomorphic functions on the open unit ball of l_1 is again the ball. For other p’s upper and lower bounds are presented that give a pretty tight description.