Unknown

Dataset Information

0

Approximately diagonalizing matrices over C(Y).


ABSTRACT: 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 closely related to the Kadison diagonal matrix question. It is also shown that this approximate diagonalization could not hold in general when dim Y ≥ 3.

SUBMITTER: Lin H 

PROVIDER: S-EPMC3286972 | biostudies-literature |

REPOSITORIES: biostudies-literature

Similar Datasets

| S-EPMC1302690 | biostudies-literature
| S-EPMC4242247 | biostudies-literature
| S-EPMC10205645 | biostudies-literature
| S-EPMC3257063 | biostudies-literature
| S-EPMC6527286 | biostudies-literature
| S-EPMC4865172 | biostudies-literature
| S-EPMC4731402 | biostudies-literature
| S-EPMC2835736 | biostudies-literature
| PRJNA1136829 | ENA
| S-EPMC1199302 | biostudies-literature