Are USA math graduate students ready for graduate school in math? I have seen some answers on this site which say that a bachelor of science in mathematics in USA is a general degree and a student needs to study other subjects as well. It also seems to me that many students who did their undergraduate in USA do not have any research experience in mathematics.

I did my undergraduate in an Australian university and it took me 4 years to complete. Each year, I had to do 8 subjects which all of them were mathematics subjects except one subject in the first year which was a programming course. I also did summer research at the end of each first three years in summer and I had to write a research thesis in the honor year (fourth year).

This makes me wonder if those people who did their undergraduate in USA are ready for graduate school because it seems that they may not have done enough mathematics subjects?

Even though I did all mathematics subjects in my undergraduate, I feel that there is some gap in my mathematics education for graduate school.

How those people who did their undergraduate in USA feel about this? do they also see this gap and that they need to work hard? 

What do I mean by ready for graduate school?

By being ready for graduate school, I mean that for instance a graduate student at university of Pennsylvania have seen all the materials in graduate preliminary exam in his undergraduate. Or if a graduate student takes any first year graduate courses, the pre-requisites for doing that course are satisfied and he does not need to learn assumed knowledge in a particular first year graduate course.
Actually, since they do make the transition regularly, the answer is yes. But that doesn't mean that they are immediately ready to take comprehensive exams or begin thesis work. 

Note that most US undergrads go to US grad schools if they move on. Each country's educational system is different. The fact that a US math major takes only about 1/3 of her/his credits in mathematics doesn't affect anything, since US grad schools expect that. 

The natural progression is to go from a BS to an MS and then to a PhD. Not all schools, however, require the master's degree for admission to the doctorate, but those that don't will have a system of courses and exams that assure that the student is ready for research when they start, whether or not an MS is part of the progression. Many schools that directly admit doctoral students will offer an MS as a painless "stepping stone" as part of the studies. Sometimes all you need to do is fill out a request form, but a short thesis or exam may also be required (as it was in my case). 

The prelim/comp exams, however, aren't based, for the most part on the undergraduate material. For example, I didn't study measure theory or delve too deeply into topology until I was a grad student. My undergrad was heavy in analysis and secondarily in algebra. But the early graduate courses built on the undergrad experience and so I was ready by the time it was necessary. But comps didn't come until late in the third year of grad study and little research was needed until that time. 

The system works as long as you stay in one country or move to a country with a similar system. Moving from an undergrad major (in any field) in the US to a grad program in UK might be a different story though, since the undergrad program in UK is much more specialized by field. 

But at the end, the students wind up in about the same place. You get a comprehensive view of the breadth of mathematics and a very deep dive into a specialized part of it so that you can do research. 

The US system isn't inferior, as the question seems to imply. It is just different.