On the absolute value of unbounded operators
On the absolute value of unbounded 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 …