Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 53
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Liu, Yongmin and Yu, Yanyan 2016. On an Extension of Stević–Sharma Operator from the General Space to Weighted-Type Spaces on the Unit Ball. Complex Analysis and Operator Theory,


    Abanin, Alexander V. and Tien, Pham Trong 2015. The algebraic equalities and their topological consequences in weighted spaces. Journal of Mathematical Analysis and Applications, Vol. 422, Issue. 1, p. 435.


    Bonet, José 2015. THE SPECTRUM OF VOLTERRA OPERATORS ON WEIGHTED SPACES OF ENTIRE FUNCTIONS. The Quarterly Journal of Mathematics, Vol. 66, Issue. 3, p. 799.


    Bonet, José and Taskinen, Jari 2015. A note about Volterra operators on weighted Banach spaces of entire functions. Mathematische Nachrichten, Vol. 288, Issue. 11-12, p. 1216.


    Gómez-Collado, M. Carmen and Jornet, David 2015. Fredholm Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions of TypeH∞. Journal of Function Spaces, Vol. 2015, p. 1.


    Hyvärinen, Olli and Nieminen, Ilmari 2015. Essential spectra of weighted composition operators with hyperbolic symbols. Concrete Operators, Vol. 2, Issue. 1,


    Li, Songxiao and Stević, Stevo 2015. Generalized weighted composition operators from α-Bloch spaces into weighted-type spaces. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,


    Liu, Yongmin Yu, Yanyan and Liu, Xiaoman 2015. Riemann–Stieltjes Operator from the General Space to Zygmund-Type Spaces on the Unit Ball. Complex Analysis and Operator Theory, Vol. 9, Issue. 5, p. 985.


    Liu, Yongmin and Yu, Yanyan 2015. Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball. Journal of Mathematical Analysis and Applications, Vol. 423, Issue. 1, p. 76.


    Beltrán, María José Bonet, José and Fernández, Carmen 2014. Classical operators on the Hörmander algebras. Discrete and Continuous Dynamical Systems, Vol. 35, Issue. 2, p. 637.


    BOYD, CHRISTOPHER and RUEDA, PILAR 2014. HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES. Journal of the Australian Mathematical Society, Vol. 96, Issue. 02, p. 186.


    Jordá, Enrique and Zarco, Ana María 2014. Weighted Banach spaces of harmonic functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, Vol. 108, Issue. 2, p. 405.


    Perfekt, Karl-Mikael 2013. Duality and distance formulas in spaces defined by means of oscillation. Arkiv för Matematik, Vol. 51, Issue. 2, p. 345.


    Ramos Fernández, Julio C. 2013. Bounded superposition operators between weighted Banach spaces of analytic functions. Applied Mathematics and Computation, Vol. 219, Issue. 10, p. 4942.


    2013. Weighted Vector-Valued Holomorphic Functions on Banach Spaces. Abstract and Applied Analysis, Vol. 2013, p. 1.


    Galindo, Pablo and Lindström, Mikael 2012. Fredholm composition operators on analytic function spaces. Collectanea Mathematica, Vol. 63, Issue. 2, p. 139.


    Liu, Yongmin and Yu, Yanyan 2012. The Multiplication Operator fromF(p,q,s)Spaces tonth Weighted-Type Spaces on the Unit Disk. Journal of Function Spaces and Applications, Vol. 2012, p. 1.


    Miralles, Alejandro 2012. Schur spaces and weighted spaces of typeH∞. Quaestiones Mathematicae, Vol. 35, Issue. 4, p. 463.


    Stević, Stevo 2012. Weighted radial operator from the mixed-norm space to the nth weighted-type space on the unit ball. Applied Mathematics and Computation, Vol. 218, Issue. 18, p. 9241.


    Stević, Stevo 2012. Norm of some operators from logarithmic Bloch-type spaces to weighted-type spaces. Applied Mathematics and Computation, Vol. 218, Issue. 22, p. 11163.


    ×
  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 54, Issue 1
  • February 1993, pp. 70-79

Biduals of weighted banach spaces of analytic functions

  • K. D. Bierstedt (a1) and W. H. Summers (a2)
  • DOI: http://dx.doi.org/10.1017/S1446788700036983
  • Published online: 01 April 2009
Abstract
Abstract

For a positive continuous weight function ν on an open subset G of CN, let Hv(G) and Hv0(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that ν f is bounded and ν f vanishes at infinity, respectively. We address the biduality problem as to when (G) is naturally isometrically isomorphic to 0(G)**, and show in particular that this is the case whenever the closed unit ball in 0(G) in compact-open dense in the closed unit ball of (G).

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Biduals of weighted banach spaces of analytic functions
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Biduals of weighted banach spaces of analytic functions
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Biduals of weighted banach spaces of analytic functions
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[5]K. D. Bierstedt , R. Meise and W. H. Summers , ‘A projective description of weighted inductive limits’, Trans. Amer. Math. Soc. 272 (1982), 107160.

[9]L. A. Rubel and J. V. Ryff , ‘The bounded weak-star topology and the bounded analytic functions’, J. Funct. Anal. 5 (1970), 167183.

[10]L. A. Rubel and A. L. Shields , ‘The space of bounded analytic functions on a region’, Ann. Inst. Fourier (Grenoble) 16 (1966), 235277.

[12]J. H. Shapiro , ‘Weak topologies on subspaces of C(S)’, Trans. Amer. Math. Soc. 157 (1971), 471479.

[13]J. H. Shapiro , ‘The bounded weak star topological and the general strict topology’, J. Funct. Anal. 8 (1971), 275286.

[15]W. H. Summers , ‘Dual spaces of weighted spaces’, Trans. Amer. Math. Soc. 151 (1970), 323333.

[16]L. Waelbroeck , ‘Duality and the injective tensor product’, Math. Ann. 163 (1966), 122126.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: