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Triangular Operators

Triangular Operators DOMINGO A. HERRERO Y es que en el mundo traidor nada hay verdad ni mentira. Todo es segun el color del cristal con que se mira. (Campoamor, ' Las dos linternas') Which operators acting on a complex, separable, infinite-dimensional Hilbert space Jf are 'the most natural analogues' of the n x n matrices acting on C ? The best answer to this question seems to be the one contained in four lines of a classical poem by Ramon de Campoamor, cited above: '... for in this treacherous world there is neither truth nor falsehood. Everything depends on the colour of the lens through which one views it.' [25, p. 175]. Since every matrix satisfies a polynomial equation, algebraic operators are good candidates. Since every complex matrix can be written as an upper triangular matrix with respect to a suitable orthonormal basis of C , triangular operators also look like good candidates (but not quite so good!). According to the colour of the particular lens of this author, the best candidates are the bitriangular operators: T admits an upper triangular matrix (with respect to some orthonormal basis of ^f) and T* is also upper triangular (with respect to another, in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Triangular Operators

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/23.6.513
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Abstract

DOMINGO A. HERRERO Y es que en el mundo traidor nada hay verdad ni mentira. Todo es segun el color del cristal con que se mira. (Campoamor, ' Las dos linternas') Which operators acting on a complex, separable, infinite-dimensional Hilbert space Jf are 'the most natural analogues' of the n x n matrices acting on C ? The best answer to this question seems to be the one contained in four lines of a classical poem by Ramon de Campoamor, cited above: '... for in this treacherous world there is neither truth nor falsehood. Everything depends on the colour of the lens through which one views it.' [25, p. 175]. Since every matrix satisfies a polynomial equation, algebraic operators are good candidates. Since every complex matrix can be written as an upper triangular matrix with respect to a suitable orthonormal basis of C , triangular operators also look like good candidates (but not quite so good!). According to the colour of the particular lens of this author, the best candidates are the bitriangular operators: T admits an upper triangular matrix (with respect to some orthonormal basis of ^f) and T* is also upper triangular (with respect to another, in

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Nov 1, 1991

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