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Semigroups of continuous module homomorphisms on complex complete random normed modules*

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Dang Hung Thang, Ta Cong Son & Nguyen Thinh

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  1. Dang Hung Thang
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  2. Ta Cong Son
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  3. Nguyen Thinh
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Correspondence to Ta Cong Son.

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* This work was supported by Vietnam National University, Hanoi (grant No. QG.16.09).

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Thang, D.H., Son, T.C. & Thinh, N. Semigroups of continuous module homomorphisms on complex complete random normed modules*. Lith Math J 59, 229–250 (2019). https://doi.org/10.1007/s10986-019-09442-z

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  • DOI: https://doi.org/10.1007/s10986-019-09442-z

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