- \tau (H_{\alpha })\;}
converges to τ ( H ) {\displaystyle \tau (H)\;} . A
tracial state is a
state τ {\displaystyle \tau } such that τ ( A B ) = τ ( B A...
- to
states or
tracial states.
Since all
states are
vacuously tracial states in the
commutative case, it is not
clear whether the
tracial condition is necessary...
-
product of a
countable number of
factors of type In with
respect to
their tracial states is the
hyperfinite type II1 factor. When n=2, this is also sometimes...
-
group is nontrivial, of type II1, i.e. it will
possess a unique, faithful,
tracial state.
Examples of ICC
groups are the
group of
permutations of an infinite...
-
finite factors (meaning the von
Neumann algebra has a
faithful normal tracial state τ : M → C {\displaystyle \tau :M\rightarrow \mathbb {C} } ). Similarly...
-
especially functional analysis, a
quasitrace is a not
necessarily additive tracial functional on a C*-algebra. An
additive quasitrace is
called a trace. It...
-
determinant using the
canonical trace. In fact,
corresponding to
every tracial state on a von
Neumann algebra there is a
notion of Fuglede−Kadison determinant...
- Heinävaara
proved a
structure theorem for
Hermitian matrices introducing tracial joint spectral measures that
implies Stahl's
theorem as a corollary. Let...
- von
Neumann algebras. For von
Neumann algebras with a
faithful normal tracial state, for
example finite von
Neumann algebras, the
notion of conditional...
-
completely positive maps. A
particular case of this
theorem corresponding to a
tracial completely positive reference map on the
matrix algebras leads to the Choi...
