The closure in a Hilbert space of a preHilbert space Chebyshev set that fails to be a Chebyshev set

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• 作者：Gordon G. Johnson ^{gjohnson10@uh.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Convex ; Unique nearest point ; Euclidean space ; Hilbert space approximation ; Chebyshev set
• 刊名：Journal of Approximation Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：28-54
• 全文大小：1701 K

文摘

In 1987 the author gave an example of a non convex Chebyshev set b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si1.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=58f0427c41ce39d4e4ca4383937376ef" title="Click to view the MathML source">S$S$ in the incomplete inner product space b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si2.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=b90f429344f336db87f5b85c167c83b5" title="Click to view the MathML source">E$E$ consisting of the vectors in b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si3.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=ab47994dcf0b6d95be1ddfbde5a86962" title="Click to view the MathML source">lb>2b> which have at most a finite number of non zero terms. In this paper, we show that the closure of b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si1.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=58f0427c41ce39d4e4ca4383937376ef" title="Click to view the MathML source">S$S$ in the Hilbert space completion b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si3.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=ab47994dcf0b6d95be1ddfbde5a86962" title="Click to view the MathML source">lb>2b> of b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si2.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=b90f429344f336db87f5b85c167c83b5" title="Click to view the MathML source">E$E$ is not Chebyshev in b=MathURL&_method=retrieve&_eid=1-s2.0-S002190451500163X&_mathId=si3.gif&_user=111111111&_pii=S002190451500163X&_rdoc=1&_issn=00219045&md5=ab47994dcf0b6d95be1ddfbde5a86962" title="Click to view the MathML source">lb>2b>.