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Zbl 1224.15066
Marcoci, A.; Marcoci, L.; Persson, L.E.; Popa, N.
Schur multiplier characterization of a class of infinite matrices. (English)
[J] Czech. Math. J. 60, No. 1, 183-193 (2010). ISSN 0011-4642; ISSN 1572-9141/e

Summary: Let $B_w(\ell ^p)$ denote the space of infinite matrices $A$ for which $A(x)\in \ell ^p$ for all $x=\{x_k\}_{k=1}^\infty \in \ell ^p$ with $\vert x_{k}\vert \searrow 0$. We characterize the upper triangular positive matrices from $B_w(\ell ^p)$, $1<p<\infty $, by using a special kind of Schur multipliers and Bennett's factorization technique. Also, some related results are stated and discussed.

MSC 2000:: *15B48
15A60 Appl. of functional analysis to matrix theory
47B35 Toeplitz operators, etc.
26D15 Inequalities for sums, series and integrals of real functions

Keywords: infinite matrix; Schur multiplier; discrete Sawyer duality principle; Bennett factorization; Wiener algebra; Hardy type inequality; upper triangular positive matrices

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