Barza, Sorina; Kravvaritis, Dimitri; Popa, Nicolae Matriceal Lebesgue spaces and Hölder inequality. (English) Zbl 1093.42002 J. Funct. Spaces Appl. 3, No. 3, 239-249 (2005). A matrix \(A=(a_{ij})\) is said to be of \(n-\)band type if \(a_{ij}=0\) for \(| i-j| >n.\) For a sequence of functions \(f=(f_l)_{l\geq1},\) let \(A_f=(a_{ij})\) where \(\widehat f_l(k)=a_{l,l+k}\) if \(k\geq0\), \(l\geq1\), and \(\widehat f_l(k)=a_{l-k,l}\) if \(k<0\), \(l\geq1\), and identify \(A_f\) with its symbol \(f\). Let \(A_f\) and \(A_g\) be two such matrices of finite band type. The authors define a commutative product of \(A_f\) and \(A_g\) as \(A_f\square A_g=A_{fg}\) and for this product prove matriceal versions of the Hölder inequality. Reviewer: Jaspal Singh Aujla (Jalandhar) Cited in 3 Documents MSC: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 26D15 Inequalities for sums, series and integrals 15B57 Hermitian, skew-Hermitian, and related matrices Keywords:Toeplitz matrices; finite band type matrices; Schur multipliers PDFBibTeX XMLCite \textit{S. Barza} et al., J. Funct. Spaces Appl. 3, No. 3, 239--249 (2005; Zbl 1093.42002) Full Text: DOI