Long chains of dense subalgebras of Banach algebras

Open Journal of Mathematical Analysis 2026 Open access

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Authors: Sidney A. Morris
DOI: 10.30538/psrp-oma2026.0186
Cited by: 0

Abstract

We construct explicit strictly ascending chains of dense subalgebras of length 𝔠 in every separable infinite-dimensional complex Banach algebra. For large classes of commutative C*-algebras we also construct strictly descending chains of the same length. The constructions rely on algebraic independence, Stone–Weierstrass arguments, and transfinite recursion.

Fields of Study & Subjects

Advanced Operator Algebra Research Advanced Banach Space Theory Holomorphic and Operator Theory

Publication details

Journal / source
Open Journal of Mathematical Analysis
Volume
10
Issue
1
Pages
82–84
Publication date
11 February 2026
Language
EN