Mercerian theorems involving Cesàro means of positive order

A. Jakimovski, D. C. Russell

Research output: Contribution to journalArticlepeer-review


If Cα denotes the Cesàro matrix of arbitrary positive order α, we investigate the set Dα of complex numbers μ for which the sequence-to-sequence transformation defined by the matrix I-μCα is equivalent to convergence. In particular, we show that Dα is strictly decreasing as α increases. Most previous investigations have taken μ real and/or α an integer; we make no such restrictions.

Original languageEnglish
Pages (from-to)119-131
Number of pages13
JournalMonatshefte fur Mathematik
Issue number2
StatePublished - Jun 1983


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