摘要：AbstractThe Collatz mapT: N* → N* is defined on the positive integers by settingT(n) equal to 3n+1/2 when n is odd and n/2 when n is even. The Collatz conjecture (or 3x+1-problem) asserts that, for any positive integer n, the orbit of n produced by iterated applications of the map T finally reaches the number 1 in a finite number of steps. In this paper, we utilize techniques from Operator Theory in order to study the conjecture. This approach enables us to “lift” the problem from the set N* to spaces of functions defined on N*, that is to sequence spaces. Hence, the study of the trajectories of the Collatz map can be related to the study of properties of bounded linear operators defined on sequence spaces.
关键词：KeywordsCollatz mapCollatz conjecturebounded linear operatorsspectral properties
