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| Re A|≤| 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.
A|| B|,| A±B|≤| A|+| B|,|| A|—| B||≤| A±B| and| Re A|≤| 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.
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.
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