What is the condition in unbounded oprerators?

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Homework Statement


T1, T2 and T3 are unbounded operators.
p_221jef11.png

What is this condition?
http://T[SUB]1[/SUB]
3. The Attempt at a Solution [/B]
T2 is the identity operator and D(T3)⊂D(T1) / D is the domain of definition.
 
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smati said:

Homework Statement


T1, T2 and T3 are unbounded operators.
p_221jef11.png

What is this condition?
http://T[SUB]1[/SUB]
3. The Attempt at a Solution [/B]
https://scontent-mrs1-1.xx.fbcdn.net/t31.0-8/13958240_283354382042877_6744203050697608959_o.jpg
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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