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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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
ID Code:1708
Deposited On:25 Mar 2009 11:42
Last Modified:01 Oct 2015 09:38

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