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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Subnormal operators, cyclic vectors and reductivity

### Tom 216 / 2013

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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