The subspace problem for weighted inductive limits of spaces of holomorphic functions
Functional Analysis
2016-09-06 v1
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.
Keywords
Cite
@article{arxiv.math/9405209,
title = {The subspace problem for weighted inductive limits of spaces of holomorphic functions},
author = {J. Bonet and Jari Taskinen},
journal= {arXiv preprint arXiv:math/9405209},
year = {2016}
}