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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1475685115

Digital Object Identifier
doi:10.1215/20088752-3661242

Mathematical Reviews number (MathSciNet)
MR3555760

Zentralblatt MATH identifier
1369.46042

Subjects
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

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

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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References

  • [1] S. J. Bhatt, Smooth Fréchet subalgebras of $C^{\star}$-algebras defined by first order differential seminorms, Proc. Indian Acad. Sci. Math. Sci. 126 (2016), no. 1, 125–141.
  • [2] A. Connes, Noncommutative Geometry, Academic Press, San Diego, 1994.
  • [3] E. Kissin and V. S. Shulman, Differential properties of some dense subalgebras of $C^{\star}$-algebras, Proc. Edinb. Math. Soc. (2) 37 (1994), no. 3, 399–422.
  • [4] T. W. Palmer, Banach Algebras and the General Theory of $\star$-algebras, I: Algebras and Banach Algebras, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, 1994.
  • [5] A. Wilansky, Summability through Functional Analysis, North-Holland Math. Stud. 85, North-Holland, Amsterdam, 1984.