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On numerical ranges of
elements of locally m-convex
algebras
John R. Giles and Donald Otto Koehler |
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Vol. 49 (1973), No. 1, 79–91
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Abstract |
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The concept of numerical range is extended from normed algebras to locally m-convex algebras. It is shown that the approximating relations between the numerical range and the spectrum of an element are preserved in the generalization. The set of elements with bounded numerical range is characterized and the relation between boundedness of the spectrum and of the numerical range is discussed. The Vidav-Palmer theory is generalized to give a characterization of b∗-algebras by numerical range. |
Mathematical Subject Classification 2000
Primary: 46H05
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Milestones
Received: 21 August 1972
Revised: 28 September 1972
Published: 1 November 1973
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Authors |
| John R. Giles | |
| Donald Otto Koehler | |
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