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Biduals of weighted banach spaces of analytic functions

  • K. D. Bierstedt (a1) and W. H. Summers (a2)
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).

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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.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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