Extremely non-complex C(K) spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:350

Article

Koszmider, Piotr²  Martin, Miguel¹  Meri, Javier¹ 

[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

[2] Politech Lodzkiej, Inst Matemat, PL-90924 Lodz, Poland

关键词: Banach space;    Few operators;    Complex structure;    Daugavet equation;    Space of continuous functions;   

DOI  :  10.1016/j.jmaa.2008.04.021

来源: Elsevier

【 摘 要 】

We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces X such that the norm equality parallel to 1d + T-2 parallel to = 1 + parallel to T-2 parallel to holds for every bounded linear operator T : X -> X. This answers in the positive Question 4.11 of [V. Kadets, M. Martin, J. Meri, Norm equalities for operators oil Banach spaces, Indiana Univ. Math. J.56 (2007) 2385-2411]. More concretely, we show that this is the case of some C(K) spaces with few operators constructed in [P. Koszmider, Banach spaces of continuous functions with few operators, Math. Ann. 330 (2004) 151-183] and [G. Plebanek, A construction of a Banach space C(K) with few operators, Topology Appl. 143 (2004) 217-239]. We also construct compact spaces K-1 and K-2 Such that C(K-1) and C(K-2) are extremely non-complex, C(K-1) contains a complemented copy of C(2(omega)) and C(K-2) contains a (1-complemented) isometric copy of l(infinity), (C) 2008 Elsevier Inc. All rights reserved.

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