Why do cookie values with whitespace arrive at the client side with quotes?

I'm a .NET developer starting to dabble in Java.

In .NET, I can set the value of a cookie to a string with white space in it: new HttpCookie("myCookieName", "my value") - and when I read that value on the client side (JavaScript), I get the value I expected (my value).

If I do the same thing in a Java servlet - new Cookie("myCookieName", "my value"), I get the value including the double quotes ("my value").

Why the difference? Am I missing something? How do people handle this in the Java world? Do you encode the value and then you decode on the client side?