Approximately diagonalizing matrices over C(Y)

作者：Lin, Huaxin^*

来源：Proceedings of the National Academy of Sciences, 2012, 109(8): 2842-2847.

DOI：10.1073/pnas.1101079108

• diagonalization
• matrix

Let X be a compact metric space which is locally absolutely retract and let phi: 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 a(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)} subset of C(Y,M-n) such that
lim(m ->infinity) Sigma(n)(i=1) f(a(i,m))p(i,m) = phi(f) for all f is an element of C(X):
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.

• 出版日期2012-2-21
• 单位华东师范大学