Elementary operators - still not elementary?

Uniform Approximation by Elementary Operators

On a separable C-algebra A every (completely) bounded map which preserves closed two sided ideals can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C-algebras of continuous sections vanishing at ∞ of locally trivial C-bundles of finite type.

Computing the Norms of Elementary Operators

We provide a direct proof that the Haagerup estimate on the completely bounded norm of elementary operators is best possible in the case of B(H) via a generalisation of a theorem of Stampfli. We show that for an elementary operator T of length `, the completely bounded norm is equal to the k-norm for k = `. A C*-algebra A has the property that the completely bounded norm of every elementary ope...

Some Formulae for Norms of Elementary Operators

We present a formula for the norm of an elementary operator on a C∗-algebra that seems to be new. The formula involves (matrix) numerical ranges and a kind of geometrical mean for positive matrices, the tracial geometric mean, which seems not to have been studied previously and has interesting properties. In addition, we characterise compactness of elementary operators. We consider an elementar...

A note on positivity of elementary operators

We show that operators on n×n matrices which are representable in the form T (X) = ∑` i=1 aiXbi (for ai and bi n×n matrices) and are k-positive for k = [ √ `] must be completely positive. As a consequence, elementary operators on a C*-algebra with minimal length ` which are k-positive for k = [ √ `] must be completely positive. For A a C*-algebra, an operator T :A→ A is called an elementary ope...

Elementary categories, elementary toposes