The authors prove statements concerning the spectrum of the difference operator of the form
is the canonical shift operator in the sequence spaces
. The same has been done by A. M. Akhmedov
and F. Baṣar
[Demonstr. Math. 39, No. 3, 585–595 (2006; Zbl 1118.47303
)] by considering
in the spaces
. Alas, all results of these papers are well-known.