Sentence examples for be continuous fields of from inspiring English sources

Let ((A_{t})_{t in Omega }) and ((B_{t})_{t in Omega }) be continuous fields of positive operators in (mathbb {A}) such that (i) (operatorname {Sp}(A_{t}) subseteq[m,M] subseteq 0,infty)) for each (t in Omega ),   (ii) the function (t mapsto Vert B_{t} Vert ) is Lebesgue integrable on Ω, and   (iii) (A_{t} B_{t} = B_{t} A_{t}) for each (t in Omega ).

Let ((A_{t})_{t in Omega }) and ((T_{t})_{t in Omega }) be two continuous fields of positive operators in (mathbb {A}) such that (operatorname {Sp}(A_{t}) subseteq[m,M] subseteq 0,infty)) for each (t in Omega ) and the function (t mapsto Vert T_{t} Vert ) is Lebesgue integrable on Ω.

Let ((A_{t})_{t in Omega }) and ((B_{t})_{t in Omega }) be two continuous fields of positive operators in (mathcal {B}(mathcal {H})) such that (operatorname {Sp}(A_{t}), operatorname {Sp}(B_{t}) subseteq[m,M] subseteq 0,infty)) for each (t in Omega ).

end{aligned} A field ((Phi_{t})_{t in Omega }) of positive linear maps from (mathbb {A}) to (mathbb {B}) is said to be a continuous field of positive linear maps if the function (t mapstoPhi_{t}(A)) is continuous on Ω for every (A in mathbb {A}).

Let ((T_{t})_{t in Omega }) be a continuous field of positive operators in (mathbb {B}) such that the function (t mapsto Vert T_{t} Vert ) is Lebesgue integrable on Ω.

Let ((W_{t})_{t in Omega }) be a continuous field of positive operators in (mathbb {A}) such that the function (t mapsto Vert W_{t} Vert ) is Lebesgue integrable on Ω.

Let ((W_{t})_{t in Omega }) be a continuous field of operators in (mathcal {B}(mathcal {H})) such that the function (t mapsto Vert W_{t} Vert ) is square integrable on Ω. Suppose that (1 in[m,M]).

Some parts of the globe parts of North America, in particular—seemed to be a continuous field of light.

Let ((Phi_{t})_{t in Omega }) be a continuous field of positive linear maps from (mathcal {B}(mathcal {H})) into (mathcal {B}(mathcal {K})) such that the function (t mapsto Vert Phi_{t}(I) Vert ) is Lebesgue integrable.

Let ((A_{t})_{t in Omega }) be a continuous field of positive definite matrices in (mathbb {M}_{k}) such that (operatorname {Sp}(A_{t}) subseteq[m,M] subseteq 0,infty)) for each (t in Omega ).

Let ((Phi_{t})_{t in Omega }) be a continuous field of positive linear maps from (mathbb {A}) into (mathbb {B}) such that the function (t mapsto Vert Phi_{t}(I) Vert ) is Lebesgue integrable.