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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.
Jacek Banasiak, and Mirosław Lachowicz. "Around the Kato generation theorem for semigroups." Studia Mathematica 179.3 (2007): 217-238. <http://eudml.org/doc/284787>.
@article{JacekBanasiak2007, abstract = {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.}, author = {Jacek Banasiak, Mirosław Lachowicz}, journal = {Studia Mathematica}, keywords = {KB-spaces; positive semigroups; perturbations of semigroups; birth-and-death problems}, language = {eng}, number = {3}, pages = {217-238}, title = {Around the Kato generation theorem for semigroups}, url = {http://eudml.org/doc/284787}, volume = {179}, year = {2007}, }
TY - JOUR AU - Jacek Banasiak AU - Mirosław Lachowicz TI - Around the Kato generation theorem for semigroups JO - Studia Mathematica PY - 2007 VL - 179 IS - 3 SP - 217 EP - 238 AB - 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. LA - eng KW - KB-spaces; positive semigroups; perturbations of semigroups; birth-and-death problems UR - http://eudml.org/doc/284787 ER -