# Proceedings of the Conference on Banach Algebras and Several by F. Greenleaf

By F. Greenleaf

Those court cases consequence from a convention on Banach Algebras and a number of advanced Variables held June 21--24, 1983, to honor Professor Charles E. Rickart upon his retirement from Yale collage. Articles current contemporary advances in a large spectrum of issues on the topic of Banach algebras, functionality algebras and endless dimensional holomorphy, parts the place Professor Rickart has made vital contributions. From a learn perspective, the articles of J. Esterle and B. Kramm are of targeted curiosity. even though the subjects during this quantity are diversified, a common wisdom of basic notions showing in Banach algebra thought will suffice for knowing such a lot articles.

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5 [27]. Let fol~owing. A be the Banach function algebra of all absolutely 39 RANGE TRANSFORMATIONS T- {z E [llzl = I} open set in n=-- 1) on the compact space 00 (the unit circle), with norm containing ~

Szeged 46 (1983), to appear. B. Aupetit and A. , to appear. , H. Cartan, Sur les zeros des combinaisons lineaires de p fonctions holomorphes donn~es, Mathematica (Cluj) 7 (1933), 5-29. Also in "Oeuvres", vol. 1. R. B. Holmes, Geometric Functional Analysis and its Applications, SpringerVerlag, 1975. 7. a. 9. ~ 10. King-Lai Hiong, Extension d'un th~or;me de M. R. Nevan1inna, GauthierVillars, 1957. 11. S. Krantz, Function Theory of Several Complex Variables, Wiley, 1982. 12. T. Nishino, Sur 1es ensembles pseudoconvexes, J.

Such that Then L u(\) = Re b(\) is analytic multi- t. 7, L(\)A is a fixed compact set E, so K(\)A = {h(\)} + E. valued on OJ. A. Zraibi and I obtained in [7] the following generalization of the Picard theorem for analytic multivalued functions: E, then either K(A)A is a K(\)A theorem and is rather complicated. that if K is analytic multivalued on is constant or the complement of the union of the sets Go-set having zero capacity. metric proof. if The original proof uses the Frostman I now intend to give an easy and more geo- As explained in the introduction, Z.