Displaying similar documents to “On the stability of strongly continuous semigroups of positive operators on L 2 ( μ ) ”

Frequently hypercyclic semigroups

Elisabetta M. Mangino, Alfredo Peris (2011)

Studia Mathematica

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We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of the semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted...

Around the Kato generation theorem for semigroups

Jacek Banasiak, Mirosław Lachowicz (2007)

Studia Mathematica

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We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in l₁ can be generalized to a larger class of the so-called Kantorovich-Banach spaces. We also present a number of related generation results that can be proved using positivity methods, as well as some examples.

Norm continuity of c 0 -semigroups

V. Goersmeyer, L. Weis (1999)

Studia Mathematica

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We show that a positive semigroup T t on L p ( Ω , ν ) with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the L p -scale, which may be of independent interest.

Hille-Yosida type theorems for local regularized semigroups and local integrated semigroups

Sheng Wang Wang (2002)

Studia Mathematica

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Motivated by a great deal of interest recently in operators that may not be densely defined, we deal with regularized semigroups and integrated semigroups that are either not exponentially bounded or not defined on [0,∞) and generated by closed operators which may not be densely defined. Some characterizations and related examples are presented. Our results are extensions of the corresponding results produced by other authors.