# The norm of an averaging operator

Ruud Martini, Gerhard F. Post

Research output: Book/ReportReportProfessional

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### 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.
Martini, Ruud ; Post, Gerhard F. / The norm of an averaging operator. Enschede : Meetkundig en toegepast-algebraisch onderzoek, 2001. 4 p. (Memorandum / Department of Applied Mathematics; 1578).
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title = "The norm of an averaging operator",
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.",
keywords = "METIS-200343, IR-65765, MSC-47B37, EWI-3398, MSC-46B45",
author = "Ruud Martini and Post, {Gerhard F.}",
note = "Imported from MEMORANDA",
year = "2001",
language = "Undefined",
isbn = "0169-2690",
series = "Memorandum / Department of Applied Mathematics",
publisher = "Meetkundig en toegepast-algebraisch onderzoek",
number = "1578",

}

Martini, R & Post, GF 2001, The norm of an averaging operator. Memorandum / Department of Applied Mathematics, no. 1578, Meetkundig en toegepast-algebraisch onderzoek, Enschede.

The norm of an averaging operator. / Martini, Ruud; Post, Gerhard F.

Enschede : Meetkundig en toegepast-algebraisch onderzoek, 2001. 4 p. (Memorandum / Department of Applied Mathematics; No. 1578).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - The norm of an averaging operator

AU - Martini, Ruud

AU - Post, Gerhard F.

N1 - Imported from MEMORANDA

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - METIS-200343

KW - IR-65765

KW - MSC-47B37

KW - EWI-3398

KW - MSC-46B45

M3 - Report

SN - 0169-2690

T3 - Memorandum / Department of Applied Mathematics

BT - The norm of an averaging operator

PB - Meetkundig en toegepast-algebraisch onderzoek

CY - Enschede

ER -

Martini R, Post GF. The norm of an averaging operator. Enschede: Meetkundig en toegepast-algebraisch onderzoek, 2001. 4 p. (Memorandum / Department of Applied Mathematics; 1578).