TY - JOUR ID - 16359 TI - Abel-Schur Multipliers on Banach Spaces of Infinite Matrices JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Popa, Nicolae AD - Institute of Mathematics of Romanian Academy, P.O. BOX 1–764 RO–014700 Bucharest, ROMANIA. Y1 - 2016 PY - 2016 VL - 2 IS - 1 SP - 39 EP - 50 KW - Abel-Schur multipliers KW - Schur multipliers KW - Toeplitz matrices KW - Bloch space of matrices DO - 10.22034/kjm.2016.16359 N2 - 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. UR - https://www.kjm-math.org/article_16359.html L1 - https://www.kjm-math.org/article_16359_bf9b78e8c1cfa9ba7ed0680a9ac595bc.pdf ER -