TY - JOUR

T1 - On Jung’s constant and related constants in normed linear spaces

AU - Amir, Dan

PY - 1985/5

Y1 - 1985/5

N2 - In this paper several results on certain constants related to the notion of Chebyshev radius are obtained. It is shown in the first part that the Jung constant of a finite-codimensional subspace of a space C(T) is 2, where T is a compact Hausdorff space which is not extremally disconnected. Several consequences are stated, e.g. the fact that every linear projection from a space C(T), T a perfect compact Hausdorff space, onto a finite-codimensional proper subspace has norm at least 2. The second discusses mainly the "self-Jung constant" which measures "uniform normal structure." It is shown that this constant, unlike Jung’s constant, is essentially determined by the finite subsets of the space.

AB - In this paper several results on certain constants related to the notion of Chebyshev radius are obtained. It is shown in the first part that the Jung constant of a finite-codimensional subspace of a space C(T) is 2, where T is a compact Hausdorff space which is not extremally disconnected. Several consequences are stated, e.g. the fact that every linear projection from a space C(T), T a perfect compact Hausdorff space, onto a finite-codimensional proper subspace has norm at least 2. The second discusses mainly the "self-Jung constant" which measures "uniform normal structure." It is shown that this constant, unlike Jung’s constant, is essentially determined by the finite subsets of the space.

UR - http://www.scopus.com/inward/record.url?scp=84972547764&partnerID=8YFLogxK

U2 - 10.2140/pjm.1985.118.1

DO - 10.2140/pjm.1985.118.1

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AN - SCOPUS:84972547764

SN - 0030-8730

VL - 118

SP - 1

EP - 15

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -