# The norm of an averaging operator

Ruud Martini, Gerhard F. Post

Research output: Book/ReportReportProfessional

### Abstract

We consider the operator $A: \ell^2 \to \ell^2$ defined by $A(a) = b$ for $a=(a_n)$ and $b=(b_n)$ with $b_n=\dfrac1n (a_1+a_2+\dots + a_n)$. We prove that $A$ has norm 2.
Original language Undefined Enschede Meetkundig en toegepast-algebraisch onderzoek 4 0169-2690 Published - 2001

### Publication series

Name Memorandum / Department of Applied Mathematics University of Twente, Department of Applied Mathematics 1578 0169-2690

• METIS-200343
• IR-65765
• MSC-47B37
• EWI-3398
• MSC-46B45

## Cite this

Martini, R., & Post, G. F. (2001). The norm of an averaging operator. (Memorandum / Department of Applied Mathematics; No. 1578). Enschede: Meetkundig en toegepast-algebraisch onderzoek.