Complex sentence: Note that there are examples of strictly singular operators whose adjoints are neither strictly singular nor strictly cosingular (see Plichko, 2004), so\\ mathcal is not in full duality with\\ mathcal.
Split into simpler sentences: Note that there are examples of strictly singular operators whose adjoints are neither strictly singular nor strictly cosingular (see Plichko, 2004). So\\ mathcal is not in full duality with\\ mathcal.