The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness, Normality and Much More

Details The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness, Normality and Much More The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness, Normality and Much More

2012-03-12

arxiv.org/abs/1203.2545v2

Mathematics

Functional Analysis

09 pages

Scientific paper

In the present paper we give results on the closedness and the self-adjointness of the sum of two unbounded operators. We present a new approach to these fundamental questions in operator theory. We also prove a new version of the Fuglede theorem where the operators involved are all unbounded. This new Fuglede theorem allows us to prove (under extra conditions) that the sum of two unbounded normal operators remains normal. Also a result on the normality of the unbounded product of two normal operators is obtained as a consequence of this new "Fuglede theorem". Some interesting examples are also given.

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