We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the L spaces associated to two von Neumann algebras M, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative L Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative L spaces.

We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the Lp spaces associated to two von Neumann algebrasM, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces.

According to Jordan Decomposition Theorem, every real function of bounded variation can be decomposed to a difference of two increasing functions. In this paper we will show, among others, that an effective version of this theorem does not hold for computable function of bounded variation.

We give the Jordan form and the Singular Value Decomposition for an integral operator N with a non-symmetric kernel N(y, z). This is used to give solutions of Fredholm equations for non-symmetric kernels, and to determine the behaviour of N n and (NN ∗)n for large n.

In this paper, we complete the classification of those finite 3groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that Z[G] satisfies MJD. In the nonabelian case, we show that Z[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.

For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.

We present a parallelization of Parlett s algorithm for computing arbitrary functions of upper triangular matrices The parallel algorithm preserves the numerical stability properties of the serial algorithm and is suitable for implementation on coarse grain parallel computers The algorithm ob tains a speedup of for matrices of size greater than as our analysis and actual implementation on a pro...

1. Introduction. One may construct a Jordan homomorphism from one (associative) ring into another ring by taking the sum of a homo-morphism and an antihomomorphism of the first ring into two ideals in the second ring with null intersection [6]. A number of authors have considered conditions on the rings that imply that every Jordan homomorphism, or isomorphism, is of this form [6], [3], [7], [1...

The work of Chevalley ([BIBLE], [Chev61]) and Demazure–Grothendieck [SGA3] provides a satisfactory understanding of the reasons for the existence and uniqueness of “Chevalley groups” over Z. These are the reductive group schemes G → Spec(Z) (i.e., smooth affine groups with connected reductive geometric fibers) for which there exists closed subtorus T ⊂ G over Z that is maximal on geometric fibe...