Subnormal operators, cyclic vectors and reductivity

Tom 216 / 2013

Béla Nagy Studia Mathematica 216 (2013), 97-109 MSC: Primary 47B20; Secondary 47B15. DOI: 10.4064/sm216-2-1

Streszczenie

Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and $^*$-cyclic vectors, and the equality $L^2(\mu )={\bf P}^2(\mu )$ for every measure $\mu $ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.

Autorzy

  • Béla NagyDepartment of Analysis
    Institute of Mathematics
    Budapest University of Technology and Economics
    H-1516 Budapest, Hungary
    e-mail

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