Titlebook: Operator Commutation Relations; Commutation Relation Palle E. T. J?rgensen,Robert T. Moore Book 1984 D. Reidel Publishing Company, Dordrech

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Exponentiation and Bounded Perturbation of Operator Lie Algebrasresent chapter contains two exponentiation theorems which are improvements upon results due to the co-authors. It also contains theorems on perturbations of Lie algebras of unbounded operators. These results are entirely new.

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Rigorous Analysis of Some Commutator Identities for Physical Observablesommutation theory with several equivalent conditions introduced by Kato [Kt 1] in his discussion of the canonical commutation relations. We indicate that generalizations of Kato’s conditions can be applied to a number of other commutation-theoretic matters that play an important role in mathematical

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The Finite-Dimensional Commutation Conditionetc. (Here A and B are endomorphisms of a dense domain D in a Banach or locally convex space E.) Below in Section 2A we distinguish several technically different ways in which this condition enters into the development. Section 2B presents examples of differential operators which satisfy the condition.

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Domain Regularity and Semigroup Commutation Relationsnsional spaces E. or D for which the exponentials in (l) can still be interpreted reasonably in terms of other endomorphisms of these spaces. As is well-known (and essentially recapitulated in Chapter 2), the standard matrix arguments using rearrangements of power series apply equally well to bounded Banach space operators A, B.