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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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