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2
votes
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Terminology for the equation $a=a+b$ in commutative semigroups

Let $(S,+)$ be a commutative semigroup. For $a,b\in S$ consider the equation $a=a+b$. Does such a relation between the given $a$ and $b$ have a name? I am currently using such equations quite often ...
2
votes
1answer
141 views

fraction power of operators in $C_0$ semigroup

Let $X$ be Banach space, and $\{Z(t)\}_{t\geq 0}\subseteq B(X)$ be the $C_0$-Semigroup of operators defined on $X$. Moreover, let $A$ be the infinitesimal generator of $\{Z(t)\}_{t\geq 0}$. A ...