The norming sets of L(mln1)

  • Sung Guen Kim Department of Mathematics, Kyungpook National University, Republic of Korea
Keywords: norming sets, multilinear forms

Abstract

UDC 517.9

Let nN, n2. An element (x1,,xn)En is called a {\em norming point} of TL(nE) if\/ x1==xn=1 and |T(x1,,xn)|=T, where L(nE) denotes the space of all continuous n-linear forms on E. For TL(nE), we define Norm(T)={(x1,,xn)En:(x1,,xn)is a norming point ofT}. The Norm(T) is called the {\em norming set} of T. For mN, m2, we characterize Norm(T) for every TL(mln1), where ln1=Rn with the l1-norm. As applications, we classify Norm(T) for every TL(mln1) with n=2,3 and m=2.

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Published
25.03.2024
How to Cite
Kim, S. G. “The Norming Sets of L(mln1)”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, no. 3, Mar. 2024, pp. 382 -94, doi:10.3842/umzh.v76i3.7294.
Section
Research articles