# Commutator, and self-commutator, approximants, 2

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Maher, Philip
(2010)
*Commutator, and self-commutator, approximants, 2.*
Filomat, 24
(4).
pp. 1-7.
ISSN 0354-5180

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Official URL: http://operator.pmf.ni.ac.rs/www/pmf/publikacije/f...

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## Abstract

We minimize the quantities (i) kT ¡ (AX ¡ XA)k, (ii) kT ¡ (X¤X ¡

XX¤)k and (iii) kT ¡ (AX ¡ XB)k where T is isometric and where in (i)

A is paranormal and commutes with T, in (ii) X¤ (or X) is paranormal

and commutes with T, and in (iii) A and B are paranormal and AT = TB

and TA = BT. The upshot is that these quantities are minimized when

0 = AX ¡XA = X¤X ¡XX¤ = AX ¡XB. To prove these results we obtain

the power norm equality for paranormal operators: if A is paranormal then

kAnk = kAkn if n 2 N.

Item Type: | Article |
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Research Areas: | A. > School of Science and Technology > Design Engineering and Mathematics |

Item ID: | 1708 |

Depositing User: | Users 36 not found. |

Date Deposited: | 25 Mar 2009 11:42 |

Last Modified: | 01 Oct 2015 09:38 |

URI: | http://eprints.mdx.ac.uk/id/eprint/1708 |

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