On the norm of a Hilbert’s type linear operator and applications

In this paper, the norm of a Hilbert’s type linear operator T : lr →lr (r > 1; r = p, q) is given. As applications, a new operator inequality and the equivalent forms with the norm are obtained, and particularly some new extended Hilbert’s type inequalities and the equivalent forms with the best constant factors are established. © 2006 Elsevier Inc. All rights reserved.