REMARKS CONCERNING SOME GENERALIZED CES (cid:18)ARO OPERATORS ON ℓ2

Abstract

Here we see that the p-Ces`aro operators, the generalized Ces`aro operators of order one, the discrete generalized Ces`aro operators, and their adjoints are all posinormal operators on ℓ2, but many of these operators are not dominant, not normaloid, and not spectraloid. The question of dominance for Ck, the generalized (cid:20) k < 1, Ces`aro operators of order one, remains unsettled when 1 2 and that points to some general questions regarding terraced matrices.

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