A “Calculus of Sequences” had started by the 1936 publication of Ward suggesting the possible range for extensions of operator calculus of Rota-Mullin, considered by several authors and after Ward. Because of convenience we shall call the Wards calculus of sequences in its afterwards elaborated form – a ψ-calculus. The notation used by Ward, Viskov, Markowsky and Roman is accommodated in confor...

The sequence spaces ?p(?q2)(0?p<?) and ??(?q2) are introduced by using the q-difference operator ?q2 of second order. Apart from studying some basic properties these spaces, we construct basis obtain ?-, ?- ?-duals spaces. Besides matrix classes involving ?p(?q2) characterized. final section is devoted to classifying spectrum over space ?1 absolutely summable sequences.