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Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topology

100%

Zagrebnov V.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019

tom 73

nr 2

The paper improves approximation theory based on the Trotter–Kato product formulae. For self-adjoint \(C_0\)-semigroups we develop a lifting of the strongly convergent Chernoff approximation (or product) formula to convergence in the operator-norm topology. This allows to obtain optimal estimate for the rate of operator-norm convergence of Trotter–Kato product formulae for Kato functions from the class \(K_2\).

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators

63%

Kanigowski A., Kryszewski W.

Open Mathematics

2012

tom 10

nr 6

2240-2263

We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Open Mathematics

1 Kanigowski A.

1 Kryszewski W.

1 Zagrebnov V.

1 2019

1 2012

Wyniki wyszukiwania

Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topology

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators