A Hardy-Davies-Petersen Inequality for a Class of Matrices
Peter D. Johnson, R. N. Mohapatra · Canadian Journal of Mathematics · 1978
Let ω be the set of all real sequences a = ﹛an﹜ n ≧0. Unless otherwise indicated operations on sequences will be coordinatewise. If any component of a has the entry oo the corresponding component of a-1 has entry zero. The convolution of two sequences s and q is given by s * q . The Toeplitz martix associated with sequence s is the lower triangular matrix defined by tnk = sn-k (n ≧ k), tnk = 0 (n < k). It can be seen that Ts(q) = s * q for each sequence q and that Ts is invertible if and only if s0 ≠ 0. We shall denote a diagonal matrix with diagonal sequence s by Ds.