Banach Journal of Mathematical Analysis

The Bass and topological stable ranks for algebras of almost periodic functions on the real line, II

Raymond Mortini and Amol Sasane

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Abstract

Let Λ be either a subgroup of the integers Z, a semigroup in N, or Λ=Q (resp., Q+). We determine the Bass and topological stable ranks of the algebras APΛ={fAP:σ(f)Λ} of almost periodic functions on the real line and with Bohr spectrum in Λ. This answers a question in the first part of this series of articles under the same heading, where it was shown that, in contrast to the present situation, these ranks were infinite for each semigroup Λ of real numbers for which the Q-vector space generated by Λ had infinite dimension.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 3 (2019), 565-581.

Dates
Received: 7 October 2018
Accepted: 26 December 2018
First available in Project Euclid: 1 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1551409236

Digital Object Identifier
doi:10.1215/17358787-2018-0051

Mathematical Reviews number (MathSciNet)
MR3978937

Zentralblatt MATH identifier
07083761

Subjects
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 42A75: Classical almost periodic functions, mean periodic functions [See also 43A60] 30H05: Bounded analytic functions

Keywords
almost periodic functions Bass stable rank topological stable rank bounded analytic functions reducibility of function pairs

Citation

Mortini, Raymond; Sasane, Amol. The Bass and topological stable ranks for algebras of almost periodic functions on the real line, II. Banach J. Math. Anal. 13 (2019), no. 3, 565--581. doi:10.1215/17358787-2018-0051. https://projecteuclid.org/euclid.bjma/1551409236


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