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Approximately diagonalizing matrices over C(Y).
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lin, Huaxin |
| Copyright Year | 2012 |
| 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. |
| File Format | PDF HTM / HTML |
| DOI | 10.1073/pnas.1101079108 |
| PubMed reference number | 22323593 |
| Journal | Medline |
| Volume Number | 109 |
| Issue Number | 8 |
| Alternate Webpage(s) | https://arxiv.org/pdf/0909.1598v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/0909.1598v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1073/pnas.1101079108 |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
