Almost inductive limit automorphisms and embeddings into AF-algebras

EMBEDDINGS INTO P(N)/fin AND EXTENSION OF AUTOMORPHISMS

Given a Boolean algebra B and an embedding e : B → P(N)/ fin we consider the possibility of extending each or some automorphism of B to the whole P(N)/ fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

On the Uniqueness of Af Diagonals in Regular Limit Algebras

Necessary and sufficient conditions are obtained for the uniqueness of standard regular AF masas in regular limit algebras up to approximate inner unitary equivalence.

Embeddings of P3-designs into bowtie and almost bowtie systems

Inductive Limit Algebras from Periodic Weighted Shifts on Fock Space

Noncommutative multivariable versions of weighted shift operators arise naturally as ‘weighted’ left creation operators acting on the Fock space Hilbert space. We identify a natural notion of periodicity for these N tuples, and then find a family of inductive limit algebras determined by the periodic weighted shifts which can be regarded as noncommutative multivariable generalizations of the Bu...

Af Embeddings and the Numerical Computation of Spectra in Irrational Rotation Algebras

The spectral analysis of discretized one-dimensional Schrödinger operators is a very difficult problem which has been studied by numerous mathematicians. A natural problem at the interface of numerical analysis and operator theory is that of finding finite dimensional matrices whose eigenvalues approximate the spectrum of an infinite dimensional operator. In this note we observe that the semina...