A Factorization Problem for Normal Completely Bounded Mappings

Factorization of Completely Bounded Bilinear Operators and Injectivity

A completely bounded bilinear operator φ: M×M → M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operators ψj , θj : M → M such that

Building a completely positive factorization

Using a bordering approach, and building upon an already known factorization of a principal block, we establish sufficient conditions under which we can extend this factorization to the full matrix. Simulations show that the approach is promising also in higher dimensions.

$n$-factorization Property of Bilinear Mappings

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

A Factorization Theorem for Logharmonic Mappings

We give the necessary and sufficient condition on sense-preserving logharmonic mapping in order to be factorized as the composition of analytic function followed by a univalent logharmonic mapping. Let D be a domain of C and denote by H(D) the linear space of all analytic functions defined on D. A logharmonic mapping is a solution of the nonlinear elliptic partial differential equation f z = a ...

Completely Regular Mappings and Dimension