On the product of class 𝐴-semigroups of linear operators

Abdelaziz, Nazar Hussein

doi:10.1090/S0002-9939-1983-0699436-3

On the product of class $A$-semigroups of linear operators
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Proc. Amer. Math. Soc. 88 (1983), 517-522 Request permission

Abstract:

The present paper extends a result of Trotter concerning the product of ${c_0}$ semigroups. We show that the product of two commuting semigroups of class $A$ is again a semigroup of class $A$ and that its generator is the sum (or its closure) of the generators of the factor semigroups. This provides a partial answer in the affirmative to a question of Hille and Phillips concerning the sum of unbounded operators [3, p. 417]. Sufficient conditions are also given in terms of the generators and their domains so that the semigroups commute.

References

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