Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]