The Daugavet equation for polynomials
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SCOPUS
- Title
- The Daugavet equation for polynomials
- Authors
- Choi, YS; Garcia, D; Maestre, M; Martin, M
- Date Issued
- 2007-03
- Publisher
- POLISH ACAD SCIENCES INST MATHEMATICS
- Abstract
- We study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality parallel to Id+P parallel to=11+parallel to P parallel to is satisfied for all weakly compact polynomials P: X -> X. We show that this is the case when X = C(K), the real or complex space of continuous functions on a compact space K without isolated points. We also study the alternative Daugavet equation max parallel to I+omega P parallel to=1+parallel to P parallel to vertical bar w vertical bar=1 for polynomials P : X -> X. We show that this equation holds for every polynomial on the complex space X = C(K) (K arbitrary) with values in X. This result is not true in the real case. Finally, we study the Daugavet and the alternative Daugavet equations for k-homogeneous polynomials.
- Keywords
- polynomial; Banach space; Daugavet equation; numerical range; BANACH-SPACES; HOLOMORPHIC-FUNCTIONS; NUMERICAL INDEX; PROPERTY; RANGE
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/23427
- DOI
- 10.4064/sm178-1-4
- ISSN
- 0039-3223
- Article Type
- Article
- Citation
- STUDIA MATHEMATICA, vol. 178, no. 1, page. 63 - 82, 2007-03
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