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  • 1 Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
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Abstract

For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of (lnm) and s(lnm), where (lnm) is the space of n-linear forms on m with the supremum norm, and s(lnm) is the subspace of (lnm) consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of (lnm) and s(lnm), respectively. We show that ext B(lnm) ⊂ ext B(lnm+1), which answers the question in []. We show that every extreme point of the unit balls of (lnm) and s(lnm) is exposed, correspondingly. We also show that

extBs(ln2)=ext B(ln2)s(ln2),
ext Bs(l2m+1)ext B(l2m+1)s(l2m+1),
expBS(ln2)=expB(ln2)s(ln2)

and expBs(l2m+1)expB(l2m+1)s(l2m+1),

which answers the questions in [].

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