operator theory...
hi,
operator theory is about developing short hand for complex calculations that can be represented by a single symbol.
an example of an operator is the upper case gamma which represents the gamma function.
so if you are reading a paper on string theory and see the upper case gamma you will know that they are talking about finding factorials of fractions.
usually operators are upper case greek letters but they can be any symbol.
i have never studied hilbert space but i would guess that is where one finds hilbert curves and other hilbert stuff too.
complex operations deals with imaginary calculus. nabla is the only operator i can think of from complex operations right now but it has been awhile since i was interested in that stuff and complex operations has operators in it. now that i think of it i is an operator for the square root of a negative number and thus qualifies as an 'operator'. so froget what i said about them always being capital greek letters.
basicaly operators prevent us from getting bogged down in arithmatic.
also operators are like '+' and '-' with the argumets to them being called operands. + and - are binomial operators which means they each take two argumets.
i am going out on a limb here but operators may be a subset of automata with the + and - being of the deterministic finite variety as is gamma. now i am not so sure about i. or pi the ratio of a radius to a half a circle. i and pi may be a nondeterministic variety of automaton.
do i sound like dale gribble yet?
sha cha...
-zander
zander
zander