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- Title
CESARO-LIKE OPERATORS.
- Authors
RHOADES, B. E.; TRUTT, D.
- Abstract
In previous work it was shown that the lower triangular generalized Hausdorff matrix Hαa with nonzero entries hnk= (n+α+1)-1, for a ≥ 0, is subnormal on Ι² if and only if α=0,1,2, …. For 0<h ≤1, the weighted Cesaro operator C'h : ..., is subnormal when .... In this paper we show that, when dj = Γ( j+1)Γ(h)/Γ( j+h), the square of the weights chosen above, then the corresponding operator Ch is bounded on Ι² for 0 < h < 3/2, that Hα is bounded on Ι² for all non-integer α < 0, and that Ch is closely related to Hh-1. This relationship leads to our main result that Ch is only subnormal when h = 1, when it corresponds to the original Cesaro operator with α = 0 and each dj = 1.
- Subjects
TRIANGULARIZATION (Mathematics); MATHEMATICS; MATHEMATICAL analysis; ALGEBRA; EQUATIONS
- Publication
Sarajevo Journal of Mathematics, 2019, Vol 15, Issue 2, p283
- ISSN
1840-0655
- Publication type
Article
- DOI
10.5644/SJM.15.02.11