I have a vague understanding of what operator, operation, function, procedure, algorithm mean in general. I am heavily biased towards computer science.
Do you agree with them? What are the generally accepted definitions that are independent of a specific field of math?
Operator is more abstract than either function or procedure; since you can add numbers,vectors,matrices,functions,sequences,etc each requireing a different procedure, but the abstract operator always has the properties of associativity ,commutativity; and function is the association between input and output ignoring the "how" and space/time complexity of procedure, but is still specific to the type of thte input and output.
operator: set of algebraic properties and an associated symbol that we may use for any function that obeys all those properties
function: subset of cartesian product of two sets such that no element of first set is used more than once
operation: function of kind (S,S)->S
procedure or algorithm: description of how to compute the dependent variable of a function when given the independent(s) and has a time/space complexity