Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Maximum modulus algebras and analytic varieties

Authors: Donna Kumagai and Zbigniew Slodkowski
Journal: Proc. Amer. Math. Soc. 112 (1991), 125-129
MSC: Primary 46J10; Secondary 32E99, 46J15
MathSciNet review: 1039534
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a maximum modulus algebra on $ X$, and $ V$ a maximal open subset of $ X$ such that $ V$ has the structure of one-dimensional variety on which functions from $ A$ are analytic. Then, the restriction algebra $ {A_{X\backslash V}}$ is again a maximum modulus algebra.

References [Enhancements On Off] (What's this?)

  • [1] B. Aupetit and J. Wermer, Capacity and uniform algebras, J. Funct. Anal. 28 (1978), 238-400. MR 496966 (80a:31001)
  • [2] T. W. Gamelin, On analytic disks in the spectrum of a uniform algebra, Arch. Math. 52 (1989), 269-274. MR 989882 (90d:46076)
  • [3] T. Nishino, Sur les ensembles pseudoconcaves, J. Math. Kyoto Univ. (1962), 225-245. MR 0147670 (26:5184)
  • [4] Z. Slodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. MR 626955 (83b:46070)
  • [5] -, Local maximum property and $ q$-plurisubharmonic functions in uniform algebras, Math. Anal. Appl. 115 (1986), 105-130. MR 835588 (87j:32050)
  • [6] J. Wermer, Potential theory and function algebras, Texas Tech. Univ. Math Series, no. 14, 1981, pp. 114-125. MR 640734 (83i:46059)
  • [7] H. Yamaguchi, Sur une uniformitte des surfaces contantes d'une fonction entiere de deux varables complexes, J. Math. Kyoto U. 13 (1973), 417-433. MR 0338424 (49:3189)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J10, 32E99, 46J15

Retrieve articles in all journals with MSC: 46J10, 32E99, 46J15

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society