Sentence examples for module actions from inspiring English sources

In this paper, we investigate the stability of (1.2) with two module actions in Banach modules over a unital -algebra.

So X is a Banach A J -bimodule with the following module actions; ( a + J ) · x = a x and x · ( a + J ) = x a, ( a ∈ A, x ∈ X ).

Then X is an A -module derivation with the following module actions: a ∗ x = λ ( a ) · x and x ∗ a = x · μ ( a ), ( a ∈ A, x ∈ X ).

Also A # is a Banach A # -bimodule with the following module actions: ( a, u ) · v = ( a · v, uv ) and v · ( a, u ) = ( v · a, vu ) ( a ∈ A, u, v ∈ A # ).

Then, ( X, ∗ ) can be considered as a Banach A - A -bimodule by the following module actions: a ∗ x = φ ( a ) · x and x ∗ a = x · φ ( a ), ( a ∈ A, x ∈ X ).

If A is (mathfrak {A} -bimodule and X is a Banach A-(mathfrak {A} -bimodulethen (andlus _1 X) is Banach (mathfrak {A})-Banachles under the module A- mathfrakgin{A- mathfrakpha.(a,x)=(alpha.a,alpha.x),(a,x).alpha =(a.alpha,x.alpha )(ain A, xin X, alpha in mathfrak {A} -module

Then H is a Hilbert module over the polynomial ring C[z] with module action p⋅f↦pf.

The data is sent up to each module, while actions (call, SMS) are sent down from the module.

In the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module VE-action.

PKA is modelled using the mass action kinetics module with the addition of the actions of the Krh proteins described earlier.

The second module is the action evaluation module based on the Bayesian inference graphs.