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The Banach‐Steinhaus theorem for the space 𝒟(ℝ) in constructive analysis
Author(s) -
Yoshida Satoru
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310031
Subject(s) - constructive , mathematics , banach space , eberlein–šmulian theorem , constructive proof , pure mathematics , space (punctuation) , discrete mathematics , lp space , computer science , process (computing) , operating system
We prove the Banach‐Steinhaus theorem for distributions on the space (ℝ) within Bishop's constructive mathematics. To this end, we investigate the constructive sequential completion $ \tilde {\cal D} $ (ℝ) of (ℝ).