Quasi-Diagonalizing Unitaries and the Generalized Weyl-Von Neumann Theorem

Shuang Zhang ()
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Shuang Zhang: University of Cincinnati, Department of Mathematical Sciences

A chapter in Algebraic Methods in Operator Theory, 1994, pp 163-171 from Springer

Abstract: Abstract We factor a quasi-diagonal unitary in the multiplier algebra M(A ⊗ K) as a product of a diagonal unitary and a perturbation of the identity by an element of A ⊗ K. This, combined with a break-through result of H. Lin [21], yields that the generalized Weyl-von Neumann theorem holds in M(A ⊗ K) if and only if K 1(A) = 0 and every unitary in M(A ⊗ K) is quasi-diagonal. In turn, PR(M(A ⊗ K)) = 0 iff K 1(A) = 0 and for each unitary u of M(A ⊗ K) there exists an approximate identity {e n} of A ⊗ K consisting of projections such that $$\parallel {{e}_{n}} - u{{e}_{n}}{{u}^{*}}\parallel \to 0$$ .

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_18

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DOI: 10.1007/978-1-4612-0255-4_18

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