Vol. 24, No. 1, 1968

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The spectral radius of averaging operators

David W. Boyd

Vol. 24 (1968), No. 1, 19–28

This paper is concerned witli tlie properties of certain operators which act on rearrangement invariant spaces of functions. The spectral radius of such an operator is determined precisely in terms of the spectral radius of the translation operator Es. A new inequality is obtained for the norm of the iterates of the averaging operator P in terms of the norm of Es.

Mathematical Subject Classification
Primary: 47.25
Secondary: 44.00
Received: 27 February 1967
Published: 1 January 1968
David W. Boyd
Department of Mathematics
University of British Columbia
Vancouver BC V6T 1Z2