English

Homage \`{a} A. M. Gleason et I. J. Schark

Complex Variables 2013-05-10 v1

Abstract

We study the maximal ideal space of H(B)H^\infty(B), where BB is the unit ball of \CCn\CC^n. Following the lead of Gleason and Schark, we analyze Gleason parts, fibers, the S\u{\i}lov boundary, and other aspects of this Banach algebra. Our work here makes good use of the inner functions construction of Aleksandrov and Hakim/L{\o} w/Sibony, particularly as formulated by Rudin.

Keywords

Cite

@article{arxiv.1305.1982,
  title  = {Homage \`{a} A. M. Gleason et I. J. Schark},
  author = {Steven G. Krantz},
  journal= {arXiv preprint arXiv:1305.1982},
  year   = {2013}
}