Calculations in new sequence spaces

Bruno de Malafosse

Address. LMAH Universit\'{e} du Havre
BP 4006 I.U.T Le Havre, 76610 Le Havre, France


Abstract. In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index $p>0$ of $r$-th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences.

AMSclassification. 40H05, 46A15.

Keywords. Infinite linear system, operator of first order difference, Banach algebra with identity, BK space.