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

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

1994-05-11

arxiv.org/abs/math/9405209v1

Mathematics

Functional Analysis

Scientific paper

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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