A semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup with an identity element is called monoid.

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Continuity of semigroups on $L^2$ and $L^1$: Is this simple proof correct?

Let $(X, \mu)$ be a $\sigma$-finite measure space, and $P_t$ a symmetric, Markovian, strongly continuous contraction semigroup on $L^2(X,\mu)$. (Markovian means that if $f \in L^2$ with $0 \le f \le ...
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1answer
111 views

Is there a special name for a semigroup whose multiplication is a constant function?

Let $S$ be a (commutative) semigroup with distinguished element 0 such that $ab=0$ for $a,b\in S.$ Of course this is a very simple family of semigroups, defined only by their cardinality. Does it ...
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1answer
73 views

Linear operators and Markov semigroups

I was trying to understand the Ergodic theory recently, but I don't really have any knowledge about linear operators, Markov semigroups etc. so I didn't even fully understand the definition. Could ...
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159 views

is there an analogue of short exact sequences for semigroups?

Since semigroups don't need to have an identity element, I was wondering if there's any kind of short exact sequence for semigroups.
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515 views

Uniqueness mild solution of $\dot{x} = A x$

Let $A$ be the infinitesimal generator of a $C_0$-semigroup $(S(t))_{t \geq 0}$. Now, for every $x_0 \in X$ the map $t \mapsto S(t) x_0$ is a mild solution of \begin{equation}\label{eq:1} \dot{x} = ...
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157 views

Semigroup with “transitive” operation is a group?

I have a semigroup $G$ (a set with associative binary operation) such that for all $a,b\in G$ there exists $x,y\in G$ such that $ax=ya=b$. Is this property enough to show that $G$ is a group, and if ...
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Are there any interesting semigroups that aren't monoids?

Are there any interesting and natural examples of semigroups that are not monoids (that is, they don't have an identity element)? To be a bit more precise, I guess I should ask if there any ...