Can bandwidth of the closed loop be bigger than bandwidth of individual elements in it?
Yes, that's perfectly possible and to be expected.

Below is a toy example that starts with a Butterworth low pass filter and puts it in the forward path of a feedback loop. The feedback path has a gain of two.

This makes the whole loop unstable, but it also makes the bandwidth very high.

The original filter's frequency response is below.



And this is the closed loop response.



R Code Below
    #30035

library("signal")

bf &lt;- butter(5, 0.1)
freqz(bf)
dev.copy(png, 'Q30035/Q30035-Butterworth.png')
dev.off()

k &lt;- 2
bf2 &lt;- bf
bf2$a &lt;- bf$a + k*bf$b
bf2$b &lt;- bf$a*k
freqz(bf2)
dev.copy(png, 'Q30035/Q30035-Feedback.png')
dev.off()