Discretization of $C^*$-algebras

Discretization of C*-algebras

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a ∗-homomorphism A → M that factors through the canonical inclusion C(X) ⊆ `∞(X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*...

On Discretization of C*-algebras

The C*-algebra of bounded operators on the separable Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through `∞(X). Consequently, there is no faithful functor discretizing C*-algebras to W*-algebras this way.

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Spatial discretization of Cuntz algebras

The (abstract) Cuntz algebra ON is generated by non-unitary isometries and has therefore no intrinsic finiteness properties. To approximate the elements of the Cuntz algebra by finite-dimensional objects, we thus consider a spatial discretization of ON by the finite sections method. For we represent the Cuntz algebra as a (concrete) algebra of operators on l2(Z+) and associate with each operato...

Fractal algebras of discretization sequences