MERCER’S THEOREMS FOR GENERALIZED SUMMABILITY METHODS IN BANACH SPACES
Tamara Sõrmus · Proceedings of the Estonian Academy of Sciences Physics Mathematics · 1998
Mercer's theorems, shortly, M-theorems, well-known for number sequences and summability methods given by scalar matrices, are generalized to larger classes of summability methods B = (B ) and sequences of points in B-spaces X.The operators By : X -X are continuous and linear on X.Seven M-theorems for generalized triangular methods and for generalized Euler-Knopp and Riesz methods of cx -cx type or £x -Zx type are presented (cx and £x being spaces of convergent sequences or absolutely convergent series).The applications of general results to scalar matrix methods and certain classical methods are also discussed.