Marie Choda

Entropy for extensions of Bernoulli shifts

We give a condition for automorphisms α and β on finite von Neumann algebras which induces the tensor product formula for entropies: H (α ⊗ β) = H (α) + H (β). As an application, the Bernoulli shift (1/n, 1/n, …, 1/n) has extensions to ergodic outer automorphisms {α k ; k = 1,2, …} on the hyperfinite II 1 factor R with the entropies H (α k ) = (1/2) kn log n .

Purely infinite, simple *-algebras arising from free product constructions. III

Certain reduced free products of C*-algebras, (A,phi)=(A_1,phi_1)*(A_2,\phi_2), taken with respect to faithful states, at least one of which is not a trace, are shown to be purely infinite and simple. It is assumed that one of the A_i contain a partial isometry in the spectral subspace of phi_i corresponding to a positive number not equal to one. For example, if A_1 and A_2 are copies of the two-by-two complex matrices and if phi_1 and phi_2 are not unitarily conjugate, it is shown that A is simple and purely infinite.

RELATIVE ENTROPY FOR MAXIMAL ABELIAN SUBALGEBRAS OF MATRICES AND THE ENTROPY OF UNISTOCHASTIC MATRICES

Let

EXTENSION ALGEBRAS OF II1 FACTORS VIA *-ENDOMORPHISMS

A

Dynamical entropy for automorphisms of exact C∗-algebras

and

Conjugate but non inner conjugate subfactors

B

CONJUGATE PAIRS OF SUBFACTORS AND ENTROPY FOR AUTOMORPHISMS

be two maximal abelian *-subalgebras of the

Entropy for automorphisms of free groups

n\times n

VON NEUMANN ENTROPY AND RELATIVE POSITION BETWEEN SUBALGEBRAS

complex matrices

A Finite Partition in a Dynamical System with Entropy Depending on the Size

M_n(\mathbb{C}).