Norm or numerical radius attaining polynomials on C(K)
SCIE
SCOPUS
- Title
- Norm or numerical radius attaining polynomials on C(K)
- Authors
- Choi, YS; Garcia, D; Kim, SG; Maestre, M
- Date Issued
- 2004-07-01
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- Let C(K, C) be the Banach space of all complex-valued continuous functions on a compact Hausdorff space K. We study when the following statement holds: every norm attaining n-homogeneous complex polynomial on C(K, C) attains its norm at extreme points. We prove that this property is true whenever K is a compact Hausdorff space of dimension less than or equal to one. In the case of a compact metric space a characterization is obtained. As a consequence we show that, for a scattered compact Hausdorff space K, every continuous n-homogeneous complex polynomial on C(K, C) can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the unit ball of C (K, E) is a norming set for every continuous complex polynomial. Similar results can be obtained if "norm" is replaced by "numerical radius." (C) 2004 Elsevier lnc. All rights reserved.
- Keywords
- EXTREME-POINTS; MULTILINEAR MAPPINGS; BILINEAR-FORMS; BANACH-SPACE; OPERATORS; DENSENESS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17867
- DOI
- 10.1016/j.jmaa.2004.03.005
- ISSN
- 0022-247X
- Article Type
- Article
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 295, no. 1, page. 80 - 96, 2004-07-01
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