A+ CATEGORY SCIENTIFIC UNIT

Around the Kato generation theorem for semigroups

Volume 179 / 2007

Jacek Banasiak, Miros/law Lachowicz Studia Mathematica 179 (2007), 217-238 MSC: 47D06, 47B60, 34G10, 92D25. DOI: 10.4064/sm179-3-2

Abstract

We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in $l_1$ 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.

Authors

  • Jacek BanasiakSchool of Mathematical Sciences
    University of KwaZulu-Natal
    Durban 4041, South Africa
    e-mail
  • Miros/law LachowiczFaculty of Mathematics, Informatics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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