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Which linear maps of
the disk algebra are multiplicative
Richard Rochberg |
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Vol. 38 (1971), No. 1, 207–212
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Abstract |
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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
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Milestones
Received: 4 February 1971
Published: 1 July 1971
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Authors |
| Richard Rochberg | |
| Department of Mathematics Washington University in St. Louis Campus Box 1146 One Brookings Dr Saint Louis MO 63130-4899 United States |
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