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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 nonsymmetric 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

abstract and applied analysis

Subnormal Weighted Shifts on Directed Trees and Composition Operators in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math><b><sup>2</sup></b>-Spaces with Nondensely Defined Powers

Subnormal Weighted Shifts on Directed Trees and Composition Operators inL2-Spaces with Nondensely Defined Powers

Subnormal Weighted Shifts on Directed Trees and Composition Operators inL²-Spaces with Nondensely Defined Powers