Vol. 53, No. 1, 1974

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Strongly bounded operators

Paul Weldon Lewis

Vol. 53 (1974), No. 1, 207–209

Recently Dobrakov, Batt and Berg, and Brooks and Lewis have studied the class of strongly bounded operators on continuous function spaces in detail. In many cases, these operators coincide with the weakly compact operators and therefore form a norm-closed two-sided ideal; and it is known in general that the strongly bounded operators form a normclosed left ideal. In this note an example is presented which shows that the strongly bounded operators do not form a right ideal.

Mathematical Subject Classification 2000
Primary: 47D15
Secondary: 47B99
Received: 15 May 1973
Published: 1 July 1974
Paul Weldon Lewis