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Subnormal operators, cyclic vectors and reductivity

100%

Nagy B.

Studia Mathematica

2013

tom 216

nr 2

97-109

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 L²(μ) = P²(μ) for every measure μ 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.

A resolvent condition implying power boundedness

63%

Nagy B., Zemánek J.

Studia Mathematica

1999

tom 134

nr 2

143-151

The Ritt and Kreiss resolvent conditions are related to the behaviour of the powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna characterization of the sublinear decay of the differences of the consecutive powers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.

Ograniczanie wyników

2 Studia Mathematica

2 Nagy B.

1 Zemánek J.

1 2013

1 1999

Wyniki wyszukiwania

Subnormal operators, cyclic vectors and reductivity

A resolvent condition implying power boundedness