Asymptotics of positive semigroups on banach lattices

Author(s):  
Wolfgang Arendt ◽  
Annette Grabosch ◽  
Günther Greiner ◽  
Ulrich Moustakas ◽  
Rainer Nagel ◽  
...  

2005 ◽  
Vol 15 (07) ◽  
pp. 1091-1117 ◽  
Author(s):  
ÀNGEL CALSINA ◽  
SÍLVIA CUADRADO

A selection mutation equations model for the distribution of individuals with respect to the age at maturity is considered. In this model we assume that a mutation, perhaps very small, occurs in every reproduction where the noncompactness of the domain of the structuring variable and the two-dimensionality of the environment are the main features. Existence of stationary solutions is proved using the theory of positive semigroups and the infinite-dimensional version in Banach lattices of the Perron Frobenius theorem. The behavior of these stationary solutions when the mutation is small is studied.





2016 ◽  
Vol 261 (5) ◽  
pp. 2607-2649 ◽  
Author(s):  
Daniel Daners ◽  
Jochen Glück ◽  
James B. Kennedy


2021 ◽  
Author(s):  
Sahiba Arora ◽  
Jochen Glück

AbstractAn intriguing feature of positive $$C_0$$ C 0 -semigroups on function spaces (or more generally on Banach lattices) is that their long-time behaviour is much easier to describe than it is for general semigroups. In particular, the convergence of semigroup operators (strongly or in the operator norm) as time tends to infinity can be characterized by a set of simple spectral and compactness conditions. In the present paper, we show that similar theorems remain true for the larger class of (uniformly) eventually positive semigroups—which recently arose in the study of various concrete differential equations. A major step in one of our characterizations is to show a version of the famous Niiro–Sawashima theorem for eventually positive operators. Several proofs for positive operators and semigroups do not work in our setting any longer, necessitating different arguments and giving our approach a distinct flavour.







1985 ◽  
Vol 32 (3) ◽  
pp. 339-343 ◽  
Author(s):  
Sadayuki Yamamuro

A theorem of T. Ando, R. Nagel and H. Uhlig on the positivity of generators of some positive semigroups in Banach lattices can not be generalized to general ordered Banach spaces.



Author(s):  
Adam Majewski ◽  
Derek W. Robinson

AbstractWe examine positive semigroups acting on Banach lattices and operator algebras. In the lattice framework we characterize strict positivity and strict ordering of holomorphic semigroups by irreducibility criteria. In the algebraic setting we derive ergodic criteria for irreducibility and discuss various aspects of strict positivity. Finally we examine invariant states of a C*-dynamical system in which the automorphism group is replaced by a strongly positive semigroup. We demonstrate that ergodic states are characterized by a cluster property despite the absence of a covariant implementation law for the semigroup.



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