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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the product of class $ A$-semigroups of linear operators


Author: Nazar Hussein Abdelaziz
Journal: Proc. Amer. Math. Soc. 88 (1983), 517-522
MSC: Primary 47D05
MathSciNet review: 699436
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699436-3
PII: S 0002-9939(1983)0699436-3
Keywords: Semigroup, linear operators, closed operator, resolvent operator, Banach space
Article copyright: © Copyright 1983 American Mathematical Society