The chi functions in generalized summability (Q910631)

In a 1971 paper, Baric defined a generalized summability analogue to the chi functional of scalar summability. His definition, valid for conservative matrices, is extended to arbitrary conservative transformations. Additionally, analogues to the functionals \(\chi_ n\) are also defined. If certain precautions are taken, the new functions \(\chi\) and \(\chi_ n\) share many of the properties of their classical counterparts and these properties are used to extend several classical results to the general setting. A necessary and sufficient condition for a conservative matrix to have a matrix inverse is obtained.