Vol. 38, No. 1, 1971

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Which linear maps of the disk algebra are multiplicative

Richard Rochberg

Vol. 38 (1971), No. 1, 207–212

Let T be a linear map of the disk algebra into itself which is of norm one and fixes the constants. This paper considers the question of what additional restrictions suffice to insure that T is multiplicative. It is shown that if T is an isometry and the range of T is a ring then T is multiplicative and that if the image under T of the coordinate function of the disk is an extreme point of the unit ball of the disk algebra then T is multiplicative.

Mathematical Subject Classification 2000
Primary: 46J15
Secondary: 30A98
Received: 4 February 1971
Published: 1 July 1971
Richard Rochberg
Department of Mathematics
Washington University in St. Louis
Campus Box 1146
One Brookings Dr
Saint Louis MO 63130-4899
United States