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Scalar spectral
operators, ordered lp-direct sums, and the counterexample
of Kakutani-McCarthy
Dieter Lutz |
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Vol. 62 (1976), No. 2, 497–505
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Abstract |
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Contrary to the situation on Hilbert space, the sum and product of two commuting scalar spectral operators on a Banach space X need not be spectral, even if X is reflexive. This has been shown by Kakutani and Mc Carthy. In this note, order-theoretic methods are used to discuss Mc Carthy’s construction. To this end, a special class of scalar spectral operators is introduced. |
Mathematical Subject Classification 2000
Primary: 47B40
Secondary: 46A40
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Milestones
Received: 18 August 1975
Revised: 8 January 1976
Published: 1 February 1976
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Authors |
| Dieter Lutz | |
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