Size of Convergence Domains for Generalized Hausdorff Prime Matrices
نویسندگان
چکیده
The convergence domain of an infinite matrix A ank n, k 0, 1, . . . will be denoted by A and is defined by A : {x {xn} | An x ∈ c}, where c denotes the space of convergence sequences, An x : ∑ k ankxk. The necessary and sufficient conditions of Silverman and Toeplitz for a matrix to be conservative are limnank ak exists for each k, limn ∑∞ k 0 ank t exists, and ||A|| : supn ∑∞ k 0 |ank| < ∞. A conservative matrix A is called multiplicative if each ak 0 and regular if, in addition, t 1. The E-J generalized Hausdorff matrices under consideration were defined independently by Endl 1, 2 and Jakimovski 3 . Each matrixH α μ is a lower triangular matrix with nonzero entries
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