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Commutativity

In: Counterexamples in Operator Theory

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  • Mohammed Hichem Mortad

    (University of Oran 1)

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.

Suggested Citation

  • Mohammed Hichem Mortad, 2022. "Commutativity," Springer Books, in: Counterexamples in Operator Theory, chapter 0, pages 465-488, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-97814-3_26
    DOI: 10.1007/978-3-030-97814-3_26
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