de Malafosse, Bruno Calculations in new sequence spaces. (English) Zbl 1164.40013 Arch. Math., Brno 43, No. 1, 1-18 (2007). The author introduces new sequence spaces using the concept of strong summability and boundedness of index \(p>0\) of \(r\)-th order difference sequences. The explicit description of these spaces requires a relatively large preliminary material, so it cannot be presented in this review. Sufficient conditions are given which guarantee that these new sequence spaces reduce to certain spaces of null and bounded sequences. Reviewer: Ondřej Došlý (Brno) MSC: 40H05 Functional analytic methods in summability 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:infinite linear system; operator of first order difference; Banach algebra with identity; BK space PDFBibTeX XMLCite \textit{B. de Malafosse}, Arch. Math., Brno 43, No. 1, 1--18 (2007; Zbl 1164.40013) Full Text: EuDML EMIS