## Annals of Functional Analysis

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

Larry B. Schweitzer

#### Abstract

We construct dense Banach subalgebras $A$ of the null sequence algebra $c_{0}$ which are spectral-invariant but do not satisfy the $D_{1}$-condition $\Vert ab\Vert _{A}\leq K(\Vert a\Vert _{\infty}\Vertb\Vert _{A}+\Vert a\Vert _{A}\Vert b\Vert _{\infty})$ for all $a,b\in A$. The sequences in $A$ vanish in a skewed manner with respect to an unbounded function $\sigma\colon{\mathbb{N}}\rightarrow[1,\infty)$.

#### Article information

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

Dates
Accepted: 20 July 2016
First available in Project Euclid: 5 October 2016

https://projecteuclid.org/euclid.afa/1475685115

Digital Object Identifier
doi:10.1215/20088752-3661242

Mathematical Reviews number (MathSciNet)
MR3555760

Zentralblatt MATH identifier
1369.46042

#### Citation

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. https://projecteuclid.org/euclid.afa/1475685115

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