Row-finite summation method
A matrix summation method determined by a row-finite matrix, that is, a matrix in which each row has only finitely many non-zero entries. An important special case of a row-finite summation method is a triangular summation method.
For every regular matrix summation method for sequences (cf. Regular summation methods), a row-finite summation method that is equivalent and compatible (see Inclusion of summation methods; Compatibility of summation methods) with it on the set of all bounded sequences can be constructed (see ). However, there exist regular matrix summation methods for which there is no equivalent row-finite summation method on the set of all sequences (see  for an example).
|||G.H. Hardy, "Divergent series" , Clarendon Press (1949)|
|||R.G. Cooke, "Infinite matrices and sequence spaces" , Macmillan (1950)|
|||A.L. Brudno, "Summation of bounded sequences by matrices" Mat. Sb. , 16 (1945) pp. 191–247 (In Russian) (English abstract)|
|||P. Erdös, G. Piranian, "Convergence fields of row-finite and row-infinite Toeplitz transformations" Proc. Amer. Math. Soc. , 1 (1950) pp. 397–401|
Row-finite summation method. I.I. Volkov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Row-finite_summation_method&oldid=17270