Vol. 22, No. 3, 1967

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A Phragmén-Lindelöf theorem for function algebras

Irving Leonard Glicksberg

Vol. 22 (1967), No. 3, 401–406

Let A be a function algebra, considered as a closed subalgebra of C(M), where M is the space of multiplicative linear functionals on A. Let denote the Šilov boundary of A. We shall call M the “interior of M” and say a function g on this “interior” is A-holomorphic if each φ in Mhas a neighborhood on which g is uniformly approximable by elements of A.

What we shall observe here is that results of the Phragmén-Lindelöf type apply to certain A-holomorphic functions.

Mathematical Subject Classification
Primary: 46.55
Received: 19 April 1966
Published: 1 September 1967
Irving Leonard Glicksberg