As I know many JEE application servers are written in Java. (JBoss, Tomcat...)
Is Websphere also written in Java?
I found that Websphere's performance is dramatic high, I guess that Websphere is written in C++. I couldn't imagine that the 'heavy' server is able to run so fast in JVM.
Is it true?
It's written in Java and in consequence portable across a wide variety of platforms including mainframes as well as Unixes and Windows.
The gap between native code and modern JVMs with JIT etc is quite small.
Yes, WebSphere is written in Java. Typically application servers used to have components orineted towards high performance (like the HTTP listeners) written in C/C++, and compiled against the various supported platforms. Nowadays, fewer application servers employ this approach and are almost always written entirely in Java (I'm not sure whether this is truly the case with WebSphere, but most of it is surely written in Java).
As for the performance of relatively better performance of WebSphere, most of it can be attributed to the performance of the IBM J9 JVM, which in contrast to the JVMs derived from Sun, is more oriented towards the server-side applications (atleast thats what some people claim, although I havent noticed a huge amount of difference).