\(L\)-matrices with lacunary coefficients. (English) Zbl 1489.15032
Summary: We show that an \(L\)-matrices \(A=[a_n]\), with lacunary coefficients \((a_n)\) is a bounded operator on \(\ell^2\), provided that \((a_n)\) satisfy an explicit decay rate. Moreover, by a concrete example, we see that the decay restriction is optimal. The extension to operators on \(\ell^p\) spaces, for \(p>1\), is also discussed.
MSC:
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
| 15A04 | Linear transformations, semilinear transformations |
| 39B42 | Matrix and operator functional equations |
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