Complex sentence: Put in another way, the kernel of a normal operator is the orthogonal complement of its range; thus, the kernel of the operator "N k" coincides with that of "N" for any "k".
Split into simpler sentences: Put in another way, the kernel of a normal operator is the orthogonal complement of its range. It follows that the kernel of the operator "N k" coincides with that of "N" for any "k".