Hello Zhihua,
Although the THS4509 can be used in a single supply configuration, I do not believe it is appropriate in this case. The THS4509 is not rail-to-rail amplifier and therefore requires split supply to keep the output centered to the ADC common mode. The output is limited to (Vs-) + 1.1V on the low side. Given the absolute maximum restriction of 1.9V on AVDD you would end up wasting most of the ADC’s dynamic range and realistically end up clipping the majority of the signal. One alternative is to use a THS4508, which is similar and pin for pin compatible with the THS4509 but the common mode range is shifted to -0.3V to 2.3V. This would give much better performance for driving the ADS4226 single supply. AC coupling is another option.
The second problem is the large amplitude range of the input. If you want 10mVpp to correspond to 2Vpp then you are talking about a gain of 200V/V. The problem comes when you amplify 1uV, the result is only 0.2mV. The ADC resolution is 12 bits, so on a 2V full scale range the ADC will only be able to resolve 0.5mV meaning the signal would be lost in the noise floor. This doesn't take into account ENOB or amplifier noise either. Additionally, the GBP required to amplify by 200V/V @ 125MHz is 25GHz which is well beyond the range of any amplifier. You may be able to cascade a couple of amps (20V/V first stage, 10V/V second stage for example) to reduce this requirement, but then you would run into problems with amplifying noise and losing accuracy for low amplitudes. Also, the EVM does not support this condition so you would need to build a new PCB. However, if you decide to go this route we offer the design files on the product page as a starting point: http://www.ti.com/litv/zip/slac459b
Hopefully this helps answer you questions.