Semigroups of continuous module homomorphisms on complex complete random normed modules

In this paper, we are concerned with a bounded strongly continuous semigroup of continuous module homomorphisms on a complex complete random normed module. The main results of this section are a theorem, which establishes a differential equation associated with the bounded s.c. semigroup generalizin...

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Veröffentlicht in:Lithuanian mathematical journal 2019-04, Vol.59 (2), p.229-250
Hauptverfasser: Thang, Dang Hung, Son, Ta Cong, Thinh, Nguyen
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we are concerned with a bounded strongly continuous semigroup of continuous module homomorphisms on a complex complete random normed module. The main results of this section are a theorem, which establishes a differential equation associated with the bounded s.c. semigroup generalizing a central result in the paper [X. Zhang and M. Liu, On almost surely bounded semigroups of random linear operators, J. Math. Phys. , 54:053517, 2013], and a theorem, which is a version of the Hille–Yosida theorem for the contraction semigroup of continuous module homomorphisms on complex complete RN module.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-019-09442-z