If you put a resistor in series with the op amp input (e.g. 10kΩ) with two small Schottky diodes, one from the input to the V+ supply (cathode), and one from the input to the V- supply (anode), the op amp should be protected from any input overvoltage without affecting the signal amplitude below that..
Thank you, crutschow, that does help.
What is the input impedance of the op amp circuit?
That I have not determined yet.
What about shifting the Non inverting input maybe 1 or 2 V "upwards"?
Otherwise, just making +Vcc higher like 9 V?
Thanks for suggestions, atferrari. No, unfortunately, I can not add DC to the signal, because I need to rectify it. Also I can not make +Vcc higher, because the power supply is 12 V single, and I am making a dual out of it with a virtual ground. And it has to be symmetrical.
But solutions proposed by rjenkinsgb and crutschow solve this problem.
Unfortunately, now I ran into another problem, and I am stuck figuring out if my project is feasible at all. Maybe it is not. I was thinking about making a peak detector that was supposed to work from 20 Hz to 1 MHz. Now it works well at low frequencies, but I see a significant signal attenuation already at 50 kHz.
I do not understand why it happens, because both the diode and the Op Amp should perform well at 1 MHz. I am reading a textbook on Op Amps now, but maybe this project is not doable at all. Thanks for the help, guys, anyway, those were good lessons for me.