Block diagonalizing ultrametric matrices

Replica Fourier Transforms on ultrametric trees , and block - diagonalizing multi - replica matrices

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4?replica matrices M ; , is shown to be dramatically simpliied through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are deened and used in the present work.

Diagonalizing Matrices

M ar 1 99 7 Replica Fourier Transforms on ultrametric trees , and block - diagonalizing multi - replica matrices

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4−replica matrices M, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work.

Diagonalizing Matrices over Aw*-algebras

Every commuting set of normal matrices with entries in an AW*algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to matrix rings is a functor on the category of AW*-

Approximately diagonalizing matrices over C(Y).

Let X be a compact metric space which is locally absolutely retract and let ϕ: C(X) → C(Y,M(n)) be a unital homomorphism, where Y is a compact metric space with dim Y ≤ 2. It is proved that there exists a sequence of n continuous maps α(i,m): Y → X (i = 1,2,…,n) and a sequence of sets of mutually orthogonal rank-one projections {p(1,m),p(2,m),…,p(n,m)} C(Y,M(n)) such that [see formula]. This is...