| Revision as of 21:16, 21 December 2011 editAnsatz (talk | contribs)93 edits →Definition: The definitions need to be distinguished for the benefit of the reader, who may well be a non-expert← Previous edit | Revision as of 22:51, 30 January 2012 edit undo94.196.111.116 (talk) →Inner product on H: new sectionNext edit → | ||
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| It needs to be made clear that a contraction operator is not in general a ] since the inequality is onlt weak. Indeed some texts, eg Kres, ''Numerical analysis'', GTM 181, use the stronger definition. ] (]) 07:36, 20 December 2011 (UTC) | It needs to be made clear that a contraction operator is not in general a ] since the inequality is onlt weak. Indeed some texts, eg Kres, ''Numerical analysis'', GTM 181, use the stronger definition. ] (]) 07:36, 20 December 2011 (UTC) | ||
| :The definitions need to be distinguished for the benefit of the reader, who may well be a non-expert. ] (]) 21:16, 21 December 2011 (UTC) | :The definitions need to be distinguished for the benefit of the reader, who may well be a non-expert. ] (]) 21:16, 21 December 2011 (UTC) | ||
| == Inner product on H == | |||
| The assertion ''The positive operator ''D<sub>T</sub>'' induces an inner product on ''H''. The space ''D<sub>T</sub>'' can be identified naturally with ''H'', with the induced inner product'' is not supported by the references cited, presumably because it is incorrect. (Consider the case when ''T'' is unitary, such as the identity: then ''D<sub>T</sub>'' is zero.) Why was this false assertion put back in the article? ] (]) 22:51, 30 January 2012 (UTC) | |||
Revision as of 22:51, 30 January 2012
This page does not specify if the operators under discussion are linear. The first link (operator norm) seems to assume linear operators. My question is, does this discussion generalize to nonlinear operators?
Definition
It needs to be made clear that a contraction operator is not in general a contraction mapping since the inequality is onlt weak. Indeed some texts, eg Kres, Numerical analysis, GTM 181, use the stronger definition. 94.197.109.147 (talk) 07:36, 20 December 2011 (UTC)
- The definitions need to be distinguished for the benefit of the reader, who may well be a non-expert. Ansatz (talk) 21:16, 21 December 2011 (UTC)
Inner product on H
The assertion The positive operator DT induces an inner product on H. The space DT can be identified naturally with H, with the induced inner product is not supported by the references cited, presumably because it is incorrect. (Consider the case when T is unitary, such as the identity: then DT is zero.) Why was this false assertion put back in the article? 94.196.111.116 (talk) 22:51, 30 January 2012 (UTC)