On Summation Processes in General

All processes which are in use to sum non-convergent sequences are particular cases of linear transformations representable by Toeplitz matrices. So far as I am aware there has been no systematic examination of the scope and limitation of processes representable by these matrices and the relation of these matrices considered as a whole to the class of all sequences on which they operate. In this paper a general study is made of these matrices without going into the special properties of any particular matrix.