On the algebra of measurable operators for a general ${\rm AW}^{\ast}$-algebra

Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra

Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies...

A Bound for the Nilpotency Class of a Lie Algebra

In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

On dimensions of derived algebra and central factor of a Lie algebra

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

Commutative Algebra Commutative Algebra : General

On Hermitian Operators over the Cayley Algebra.

With the aid of equations (72) and (76) we can determine the horizontal displacement q(t), using its operational representation given in equation (65). 4. Summary.-An exact solution is given for the motion of the surface of a uniform elastic half-space produced by a point pressure pulse situated at a depth H below the surface. The time variation of the pressure pulse is assumed to be given by t...