## Taiwanese Journal of Mathematics

### GENERATION OF LOCAL $C$-SEMIGROUPS AND SOLVABILITY OF THE ABSTRACT CAUCHY PROBLEMS

#### Abstract

For a bounded linear injection $C$ on a Banach space $X$ and a (not necessarily densely defined) closed linear operator $A$ which commutes with $C$, we present various conditions for $A$ to generate a local $C$-semigroup. A Hille-Yosida type generation theorem in terms of the asymptotic $C$-resolvent of $A$ is proved, and various characterizations of a generator by means of existence of unique strong solutions of the associated abstract Cauchy problems are obtained.

#### Article information

Source
Taiwanese J. Math., Volume 9, Number 2 (2005), 291-311.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407804

Digital Object Identifier
doi:10.11650/twjm/1500407804

Mathematical Reviews number (MathSciNet)
MR2142579

Zentralblatt MATH identifier
1096.47050

#### Citation

Shaw, Sen-Yen; Kuo, Chung-Cheng. GENERATION OF LOCAL $C$-SEMIGROUPS AND SOLVABILITY OF THE ABSTRACT CAUCHY PROBLEMS. Taiwanese J. Math. 9 (2005), no. 2, 291--311. doi:10.11650/twjm/1500407804. https://projecteuclid.org/euclid.twjm/1500407804

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