Commutator, and self-commutator, approximants, 2

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

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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
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 1708
Depositing User: Repository team
Date Deposited: 25 Mar 2009 11:42
Last Modified: 15 Feb 2016 15:04
URI: http://eprints.mdx.ac.uk/id/eprint/1708

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