Large Perturbations of Nest Algebras

2024/08/06 by Kenneth R. Davidson, Davidson, Kenneth R.
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2408.03317

Abstract

Let M and N be nests on separable Hilbert space. If the two nest algebras are distance less than 1 (d(T(M),T(N)) < 1), then the nests are distance less than 1 (d(M,N)<1). If the nests are distance less than 1 apart, then the nest algebras are similar, i.e. there is an invertible S such that SM = N, so that S T(M)S^-1 = T(N). However there are examples of nests closer than 1 for which the nest algebras are distance 1 apart.

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