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The subspace problem for weighted inductive limits of spaces of holomorphic functions

J. Bonet·Jari Taskinen
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Abstract

We construct a countable inductive limit of weighted Banach spaces of holomorphic functions, which is not a topological subspace of the corresponding weighted inductive limit of spaces of continuous functions. The main step of our construction, using a special sequence of outer holomorphic functions, shows that a certain sequence space is isomorphic to a complemented subspace of a weighted space of holomorphic functions in two complex variables. This example solves in the negative a well-known open problem raised by Bierstedt, Meise and Summers.

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J. Bonet, Jari Taskinen. 1994-05-11. The subspace problem for weighted inductive limits of spaces of holomorphic functions. https://arxiv.org/abs/math/9405209

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