1,373 research outputs found
A reduction theorem for capacity of positive maps
We prove a reduction theorem for capacity of positive maps of finite
dimensional C*-algebras, thus reducing the computation of capacity to the case
when the image of a nonscalar projection is never a projection.Comment: 7 page
A survey of noncommutative dynamical entropy
The paper is a survey of dynamical entropy of automorphisms of operator
algebras. We describe the different entropies of Connes-Stormer,
Connes-Narnhofer-Thirring, Sauvageot-Thouvenot, and Voiculescu, and discuss
the main examples of the theory.Comment: 48 pages, late
Why Can’t Tyrone Write: Reconceptualizing Flower and Hayes for African-American Adolescent Male Writers
Using qualitative methods and a case study design, the perceptions and writing processes of three African-American eighth grade males were explored. Data were derived from semi-structured and informal interviews; and document analysis. The study concluded that the perceptions of the three participants’ writing processes did not adhere to the steps depicted by the cognitive process model of writing (Flower and Hayes, 1981) that has become a dominant model for describing the composing processes of students. Recommendations are made for altering the Flower and Hayes model to depict how these three, African-American eighth graders perceive school writing
Separable states and the SPA of a positive map
We introduce a nessecary condition for a state to be separable and apply this
condition to the SPA of an optimal ositive map and give a proof of the fact
that the SPA need not be the density ooperator for a separable state
Multiplicative properties of positive maps
Let be a positive unital normal map of a von Neumann algebra into
itself, and assume there is a family of normal -invariant states which is
faithful on the von Neumann algebra generated by the image of . It is
shown that there exists a largest Jordan subalgebra of such that
the restriction of to is a Jordan automorphhism, and each weak
limit point of for belongs to .Comment: 8 page
Asymptotic lifts of positive linear maps
We show that the notion of asymptotic lift generalizes naturally to normal
positive maps acting on von Neumann algebras M.
We focus on cases in which the domain of the asymptotic lift can be embedded
as an operator subsystem of M, and characterize when that subsystem is a Jordan
subalgebra of M in terms of the asymptotic multiplicative properties of .Comment: 13 page
The variational principle for a class of asymptotically abelian C*-algebras
Let (A,\alpha) be a C*-dynamical system. We introduce the notion of pressure
P_\alpha(H) of the automorphism \alpha at a self-adjoint operator H\in A. Then
we consider the class of AF-systems satisfying the following condition: there
exists a dense \alpha-invariant *-subalgebra \A of A such that for all pairs
a,b\in\A the C*-algebra they generate is finite dimensional, and there is
p=p(a,b)\in\N such that [\alpha^j(a),b]=0 for |j|\ge p. For systems in this
class we prove the variational principle, i.e. show that P_\alpha(H) is the
supremum of the quantities h_\phi(\alpha)-\phi(H), where h_\phi(\alpha) is the
Connes-Narnhofer-Thirring dynamical entropy of \alpha with respect to the
\alpha-invariant state \phi. If H\in\A, and P_\alpha(H) is finite, we show that
any state on which the supremum is attained is a KMS-state with respect to a
one-parameter automorphism group naturally associated with H. In particular,
Voiculescu's topological entropy is equal to the supremum of h_\phi(\alpha),
and any state of finite maximal entropy is a trace.Comment: LaTeX2e, 20 page
Ergodic theory and maximal abelian subalgebras of the hyperfinite factor
Let T be a free ergodic measure-preserving action of an abelian group G on
(X,mu). The crossed product algebra R_T has two distinguished masas, the image
C_T of L^infty(X,mu) and the algebra S_T generated by the image of G. We
conjecture that conjugacy of the singular masas S_{T^(1)} and S_{T^(2)} for
weakly mixing actions T^(1) and T^(2) of different groups implies that the
groups are isomorphic and the actions are conjugate with respect to this
isomorphism. Our main result supporting this conjecture is that the conclusion
is true under the additional assumption that the isomorphism gamma of R_{T^(1)}
onto R_{T^(2)} such that gamma(S_{T^(1)})=S_{T^(2)} has the property that the
Cartan subalgebras gamma(C_{T^(1)}) and C_{T^(2)} of R_{T^(2)} are inner
conjugate. We discuss a stronger conjecture about the structure of the
automorphism group Aut(R_T,S_T), and a weaker one about entropy as a conjugacy
invariant. We study also the Pukanszky and some related invariants of S_T, and
show that they have a simple interpretation in terms of the spectral theory of
the action T. It follows that essentially all values of the Pukanszky invariant
are realized by the masas S_T, and there exist non-conjugate singular masas
with the same Pukanszky invariant.Comment: LaTeX2e, 18
- …