Abstract
Conditions are found under which the norm of an operator on a Banach sequence space is determined by its action on decreasing, positive sequences. For the space $d(w,1)$, the norm and “lower bound” of such operators can be equated to the supremum and infimum of a certain sequence. These quantities are evaluated for the averaging, Copson and Hilbert operators, with the weighting sequence given either by $w = 1/n^{\alpha}$ or by the corresponding integral.
Citation
G. J. O. Jameson. "Norms and lower bounds of operators on the Lorentz sequence space $d(w,1)$." Illinois J. Math. 43 (1) 79 - 99, Spring 1999. https://doi.org/10.1215/ijm/1255985338
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