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Zbl 0588.47048
Kraus, Jon; Larson, David R.
Some applications of a technique for constructing reflexive operator algebras.
(English)
[J] J. Oper. Theory 13, 227-236 (1985). ISSN 0379-4024

Let H be a Hilbert space and A an algebra of operators in L(H). For certain such algebras (e.g. nest algebras) it is known that there is a constant K so that the distance from any operator T in L(H) to A satisfies d(T,A)$\le K \sup \{\Vert P\sp{\perp}TP\Vert \vert$ $P\in lat A\}$, where lat A denotes the lattice of invariant subspaces for A (see the paper under review for appropriate references). \par In this paper an example is given of a reflexive algebra which does not satisfy such a distance estimate, thereby answering a question posed by several authors. The construction is based on a general technique which can be modified to produce other interesting examples and counter- examples.
[J.R.Holub]
MSC 2000:
*47L30 Abstract operator algebras on Hilbert spaces
47A15 Invariant subspaces of linear operators

Keywords: nest algebras; lattice of invariant subspaces; reflexive algebra; distance estimate

Cited in: Zbl 1232.47006

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