If I have a function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

f:R\rightarrow L

[/tex]

where L is the space of linear operators from an hilbert space to itself, how can i define the derivative of f at a particular point of R? I mean, it is "obvious" that one should try:

[tex]

f'(s_0)=lim_{\Delta s\rightarrow0}\frac{|f(s_0 + \Delta s) -f(s_0)|}{\Delta s}

[/tex]

but i'm concerned with the fact that when in the numerator i use ||, i mean the norm on L, which as i said is the space of linear operators from an hilbert space to itself. Since in physics one often deals with operators that have infinite operator norm, I wanted to know if the norm of that difference of operators is finite or not, even if we take unbounded operators.

It is a mathematical question, but since in QM one encounters these things all the time, I wanted some clarifications..

thanks!

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# Derivative of an operator valued function

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