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Do someone knows this notation $\dot{=}$? I'm studying Amann's book and he uses this notation but I couldn't find a definition in his book. For example, he writes $$E_1\cap E_0\dot{=}E_1\ and \ E_0+E_1\dot{=}E_0 \ if \ E_1\hookrightarrow E_0.$$

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  • $\begingroup$ "approximately equal to" ? As far as I know. also see en.wikipedia.org/wiki/Equals_sign $\endgroup$ – J. Yu Mar 9 '16 at 8:37
  • $\begingroup$ In the abstract evolution equations literature, this is symbol usually means equivalence in the sense of Banach spaces (equal as vector spaces and having equivalent norms). $\endgroup$ – user135971 Aug 3 '16 at 14:38
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According to Wikipedia it is a symbol used for definitions like $\equiv$ or similar symbols.

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  • $\begingroup$ I think that it. He also uses the symbol $:=$, so I believe that it means "is defined as" and as you said $\doteq$ means "is equivalent to ". Thank you. $\endgroup$ – Reginaldo Demarque da Rocha Mar 9 '16 at 9:12

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