Vol. 62, No. 2, 1976

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ISSN: 0030-8730
Scalar spectral operators, ordered lp-direct sums, and the counterexample of Kakutani-McCarthy

Dieter Lutz

Vol. 62 (1976), No. 2, 497–505
Abstract

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
Milestones
Received: 18 August 1975
Revised: 8 January 1976
Published: 1 February 1976
Authors
Dieter Lutz