In this paper, we show the invariance of Fredholm index non-smooth pseudodifferential operators with coefficients in Hölder spaces. By means invariance, improve previous spectral results for [Formula: see text] For purpose, approximate smooth and use a result operators. Then, get analogy to proof differential by Rabier.

The main purpose of this paper is to characterize the compact, invertible, Fredholm and closed range multiplication operators on second Ces\`{a}ro-Orlicz sequence spaces.