Subnormal weighted shifts on directed trees and composition operators in L² spaces with non-densely defined powers

الأصل · EN

It is shown that for every positive integer n there exists a subnormal weighted shift on a directed tree (with or without root) whose nth power is densely defined while its (n+1)th power is not. As a consequence, for every positive integer n there exists a non-symmetric subnormal composition operator C in an L² space over a σ-finite measure space such that Cⁿ is densely defined and Cⁿ⁺¹ is not.