Annals of Functional Analysis

Dense Banach subalgebras of the null sequence algebra which do not satisfy a differential seminorm condition

Larry B. Schweitzer

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We construct dense Banach subalgebras A of the null sequence algebra c0 which are spectral-invariant but do not satisfy the D1-condition abAK(abA+aAb) for all a,bA. The sequences in A vanish in a skewed manner with respect to an unbounded function σ:N[1,).

Article information

Ann. Funct. Anal., Volume 7, Number 4 (2016), 686-690.

Received: 12 May 2016
Accepted: 20 July 2016
First available in Project Euclid: 5 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L87: Noncommutative differential geometry [See also 58B32, 58B34, 58J22]
Secondary: 46H10: Ideals and subalgebras 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 46B45: Banach sequence spaces [See also 46A45] 46K99: None of the above, but in this section

$D_{1}$-subalgebra spectral invariance null sequence algebra differential structure in $C^{\star}$-algebras


Schweitzer, Larry B. Dense Banach subalgebras of the null sequence algebra which do not satisfy a differential seminorm condition. Ann. Funct. Anal. 7 (2016), no. 4, 686--690. doi:10.1215/20088752-3661242.

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