Popa, N. (2016). Abel-Schur Multipliers on Banach Spaces of Infinite Matrices. Khayyam Journal of Mathematics, 2(1), 39-50. doi: 10.22034/kjm.2016.16359

Nicolae Popa. "Abel-Schur Multipliers on Banach Spaces of Infinite Matrices". Khayyam Journal of Mathematics, 2, 1, 2016, 39-50. doi: 10.22034/kjm.2016.16359

Popa, N. (2016). 'Abel-Schur Multipliers on Banach Spaces of Infinite Matrices', Khayyam Journal of Mathematics, 2(1), pp. 39-50. doi: 10.22034/kjm.2016.16359

Popa, N. Abel-Schur Multipliers on Banach Spaces of Infinite Matrices. Khayyam Journal of Mathematics, 2016; 2(1): 39-50. doi: 10.22034/kjm.2016.16359

Abel-Schur Multipliers on Banach Spaces of Infinite Matrices

^{}Institute of Mathematics of Romanian Academy, P.O. BOX 1–764 RO–014700 Bucharest, ROMANIA.

Abstract

We consider a more general class than the class of Schur multipliers namely the Abel-Schur multipliers, which in turn coincide with the bounded linear operators on $\ell_{2}$ preserving the diagonals. We extend to the matrix framework Theorem 2.4 (a) of a paper of Anderson, Clunie, and Pommerenke published in 1974, and as an application of this theorem we obtain a new proof of the necessity of an old theorem of Hardy and Littlewood in 1941.