Bonded projections, duality, and multipliers in spaces of analytic functions

Authors:
A. L. Shields and D. L. Williams

Journal:
Trans. Amer. Math. Soc. **162** (1971), 287-302

MSC:
Primary 46.30; Secondary 30.00

DOI:
https://doi.org/10.1090/S0002-9947-1971-0283559-3

MathSciNet review:
0283559

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Abstract: Let and be positive continuous functions on with as and . Denote by and the Banach spaces of functions *f* analytic in the open unit disc *D* with and , respectively. In both spaces . Let denote the space of functions analytic in *D* with . The spaces , and are identified in the obvious way with closed subspaces of , and , respectively. For a large class of weight functions which go to zero at least as fast as some power of but no faster than some other power of , we exhibit bounded projections from onto , from onto , and from onto . Using these projections, we show that the dual of is topologically isomorphic to for an appropriate, but not unique choice of . In addition, is topologically isomorphic to the dual of . As an application of the above, the coefficient multipliers of , and are characterized. Finally, we give an example of a weight function pair for which some of the above results fail.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0283559-3

Keywords:
Banach spaces,
analytic functions,
projections,
topological direct sums,
multiplier transforms

Article copyright:
© Copyright 1971
American Mathematical Society