The norm of an averaging operator

Ruud Martini, Gerhard F. Post

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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 languageUndefined
Place of PublicationEnschede
PublisherMeetkundig en toegepast-algebraisch onderzoek
Number of pages4
ISBN (Print)0169-2690
Publication statusPublished - 2001

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.1578
ISSN (Print)0169-2690

Keywords

  • 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.