The primary purpose of the present paper is to investigate when relations of the types |AB| = |A||B|, |A ± B| ≤ |A| + |B|, ||A| − |B|| ≤ |A ± B| and |ReA| ≤ |A| (among others) hold in an unbounded operator setting. As interesting consequences, we obtain a characterization of (unbounded) self-adjointness as well as a characterization of invertibility for the class of unbounded normal operators.
The primary purpose of the present paper is to investigate when relations of the types |AB|=|A||B|, |A±B|⩽|A|+|B|, ||A|−|B||⩽|A±B| and |¯¯¯¯¯¯¯¯¯¯¯ReA|⩽|A| (among others) hold in an unbounded operator setting. As consequences, we obtain a characterization of (unbounded) self-adjointness as well as a characterization of invertibility for the class of unbounded normal operators. Some examples accompany our results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.