Regex - Does not contain certain Characters

^[^<>]+$

The caret in the character class ([^) means match anything but, so this means, beginning of string, then one or more of anything except < and >, then the end of the string.

Here you go:

^[^<>]*$

This will test for string that has no < and no >

If you want to test for a string that may have < and >, but must also have something other you should use just

[^<>] (or ^.*[^<>].*$)

Where [<>] means any of < or > and [^<>] means any that is not of < or >.

And of course the mandatory link.