Commutativity

Mohammed Hichem Mortad
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Mohammed Hichem Mortad: University of Oran 1

Chapter Chapter 26 in Counterexamples in Operator Theory, 2022, pp 465-488 from Springer

Abstract: Abstract We have already introduced the concept of commutativity of a bounded operator with an unbounded one. In the case of two densely defined operators A and B, things are more delicate. Indeed, a major obstacle is that AB − BA may only be defined on {0} as we have already observed on many occasions. The remark below the integral form of the spectral theorem for (bounded) self-adjoint operators is the definition we are adopting in the unbounded case. Notice that we have already touched on this definition implicitly in some cases.

Date: 2022
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DOI: 10.1007/978-3-030-97814-3_26

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