Sentence examples for be a commutative semigroup from inspiring English sources

Let G be a commutative semigroup, K = R or ℂ and F : G → K n.

Let Let be a commutative semigroup, and a complete Abelian metric group.

Let (S, + ) be a commutative semigroup and f,g :S→ C satisfying ∥ f ( x + y ) − g ( y ) f ( x ) ∥ ≤ δ Open image in new window (3.10).

We now let S be a commutative semigroup and define a partial order ≽ on S by s ≽ t if s = t or there exists u ∈ S such that s = ut.

Let ( X, + ) be a commutative semigroup, Y be a Banach space and ε > 0. Then for every g : X → Y with sup x, y ∈ X ∥ g ( x + y ) − g ( x ) − g ( y ) ∥ ≤ ε there is a unique f : X → Y such that sup x ∈ X ∥ g ( x ) − f ( x ) ∥ ≤ ε and f ( x + y ) = f ( x ) + f ( y ), x, y ∈ X. (1).

Then g is either bounded or f(x + y)= g y)f(x) for all x,y∈ S. Let (S, + ) be a commutative semigroup and f : S→ C satisfying ∥ f ( x + y ) − f ( y ) f ( x ) ∥ ≤ δ Open image in new window (3.11).

Let (S, + ) be an commutative semigroup and f, g : S → C Open image in new window satisfying ∥ f ( x + y ) − g ( y ) f ( x ) ∥ ≤ ϕ ( x, y ) Open image in new window (3.8).

for all where is a commutative semigroup.

As is well known, B(S) is amenable when S is a commutative semigroup, see [15].

As it is well known, is amenable when is a commutative semigroup; see [12].

As is well known, is amenable when it is a commutative semigroup [12].