On diagonal operators between the sequence (LF)-spaces $$l_p({\mathcal {V}})$$
On diagonal operators between the sequence (LF)-spaces $$l_p({\mathcal {V}})$$
Abstract Diagonal (multiplication) operators acting between a particular class of countable inductive spectra of Fréchet sequence spaces, called sequence (LF)-spaces, are investigated. We prove results concerning boundedness, compactness, power boundedness, and mean ergodicity. Furthermore, we determine when a diagonal operator is Montel and reflexive. We analyze the spectra in terms …