Norms and lower bounds of operators on the Lorentz sequence space $d(w,1)$
Jameson, G. J. O.
Illinois J. Math., Tome 43 (1999) no. 3, p. 79-99 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1999-03-15
Classification:  47B37,  26D15,  46B45,  47A30 
@article{1255985338,
     author = {Jameson, G. J. O.},
     title = {Norms and lower bounds of operators on the Lorentz sequence space $d(w,1)$},
     journal = {Illinois J. Math.},
     volume = {43},
     number = {3},
     year = {1999},
     pages = { 79-99},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255985338}
}

Jameson, G. J. O. Norms and lower bounds of operators on the Lorentz sequence space $d(w,1)$. Illinois J. Math., Tome 43 (1999) no. 3, pp.  79-99. http://gdmltest.u-ga.fr/item/1255985338/