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A Bounded Closed Convex Set in c0(ℂ) without Modulus Support Functionals

  • Xin Luo
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Abstract

We construct a bounded closed convex set in c0(ℂ) on which no nonzero continuous complex-linear functional attains its maximum modulus. Consequently, this answers in the negative the two longstanding questions raised by Deville, Godefroy and Zizler in \cite[p. 35]{DGZ}. The construction uses a small perturbation of the identity on c0(ℝ).

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Cite

BibTeXRIS
BibTeX
@misc{luo2026bounded,
  title = {{A Bounded Closed Convex Set in $c_0(\mathbbC)$ without Modulus Support Functionals}},
  author = {Xin Luo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36771},
  eprint = {2610.36771},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36771},
}
RIS
TY  - UNPB
TI  - A Bounded Closed Convex Set in c_0(ℂ) without Modulus Support Functionals
AU  - Xin Luo
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36771
UR  - https://arxiv.org/abs/2610.36771
AB  - We construct a bounded closed convex set in c_0(ℂ) on which no nonzero continuous complex-linear functional attains its maximum modulus. Consequently, this answers in the negative the two longstanding questions raised by Deville, Godefroy and Zizler in \cite[p. 35]{DGZ}. The construction uses a small perturbation of the identity on c_0(ℝ).
ER  -