Sentence examples for a unitary element from inspiring English sources

These equations show clearly that the vehicle, even if divided into subsystems and internal functional blocks are a unitary element.

The C⁎-algebra of this dynamical system is generated by functions in C X) and a unitary element u implementing the action.

Let M be a von Neumann algebra and let β be a nest in M. We consider the problem of factoring an invertible element S of M as S = WA, where W is a unitary element in M and both A and A−1 are elements of M which also belong to Alg.

Let M be a W⁎-algebra and let LS(M) be the algebra of all locally measurable operators affiliated with M. It is shown that for any self-adjoint element a∈LS(M) there exists a self-adjoint element c0 from the center of LS(M), such that for any ε>0 there exists a unitary element uε from M, satisfying |[a,uε]|⩾(1−ε)|a−c0|.

We give examples of such endomorphisms λ="λu for which the associated unitary element u in On (which satisfies λ(Sj)="uSj for all j) does not belong to Fn.

Furthermore, R is given by a "Dixmier process" in which the averaging is effected by a group of unitary elements in the centre of the multiplier algebra M(B).

Let U ( A ) be the set of unitary elements in A. We investigate C ∗ -algebra isomorphisms in unital multi- C ∗ -algebras.

for all and all Since is -linear and each is a finite linear combination of unitary elements, that is, where and for all it follows from (3.11) that (3.12).

for all and all So and for all and all Since is -linear and each is a finite linear combination of unitary elements (see [57]), that is, where and for all we have (3.6).

Since H is ℂ-linear and each x ∈ X is a finite linear combination of unitary elements, i.e., x = ∑ j = 1 m λ j u j ( λ j ∈ C, u j ∈ U X X ) ), it follows from (15) that H ( x v ) = H ( ∑ j = 1 m λ j u j v ) = ∑ j = 1 n λ j H ( u j v ) = ∑ j = 1 n λ j H ( u j ) H ( v ) = H ( ∑ j = 1 m λ j u j ) H ( v ). for all v ∈ U X X ).

Since H is C -linear and each x ∈ X is a finite linear combination of unitary elements, i.e., x = ∑ j = 1 m λ j u j ( λ j ∈ C, u j ∈ U X X ) ), it follows from (4.3) that H ( x v ) = H ( ∑ j = 1 m λ j u j v ) = �� j = 1 n λ j H ( u j v ) = ∑ j = 1 n λ j H ( u j ) H ( v ) = H ( ∑ j = 1 m λ j u j ) H ( v ). for all v ∈ U X X ).