Asymptotics of positive semigroups on banach lattices

1986 ◽  
pp. 333-367
Author(s):  
Wolfgang Arendt ◽  
Annette Grabosch ◽  
Günther Greiner ◽  
Ulrich Moustakas ◽  
Rainer Nagel ◽  
...  
Keyword(s):  
Banach Lattices ◽  
Positive Semigroups

STATIONARY SOLUTIONS OF A SELECTION MUTATION MODEL: THE PURE MUTATION CASE

2005 ◽  
Vol 15 (07) ◽  
pp. 1091-1117 ◽  
Author(s):  
ÀNGEL CALSINA ◽  
SÍLVIA CUADRADO
Keyword(s):  
Stationary Solutions ◽  
Banach Lattices ◽  
Age At Maturity ◽  
Frobenius Theorem ◽  
Positive Semigroups ◽  
Infinite Dimensional ◽  
Mutation Model ◽  
Dimensional Version

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.

On the peripheral spectrum of bounded positive semigroups on atomic Banach lattices

2006 ◽  
Vol 87 (4) ◽  
pp. 359-367 ◽  
Author(s):  
Vera Keicher
Keyword(s):  
Banach Lattices ◽  
Peripheral Spectrum ◽  
Positive Semigroups

scholarly journals Eventually and asymptotically positive semigroups on Banach lattices

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

scholarly journals Spectrum and convergence of eventually positive operator semigroups

2021 ◽  
Author(s):  
Sahiba Arora ◽  
Jochen Glück
Keyword(s):  
Differential Equations ◽  
Positive Operator ◽  
Positive Operators ◽  
Banach Lattices ◽  
Time Behaviour ◽  
Major Step ◽  
Operator Semigroups ◽  
Positive Semigroups ◽  
Long Time Behaviour ◽  
Long Time

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.

Spectral Properties of a Class of Positive Semigroups on Banach Lattices and Streaming Operators

Positivity ◽  
2006 ◽  
Vol 10 (2) ◽  
pp. 231-249 ◽  
Author(s):  
Mustapha Mokhtar-Kharroubi
Keyword(s):  
Spectral Properties ◽  
Banach Lattices ◽  
Positive Semigroups

Triviality of the Peripheral Point Spectrum of Positive Semigroups on Atomic Banach Lattices

Positivity ◽  
2007 ◽  
Vol 12 (1) ◽  
pp. 185-192 ◽  
Author(s):  
Manfred P. H. Wolff
Keyword(s):  
Point Spectrum ◽  
Banach Lattices ◽  
Positive Semigroups ◽  
Peripheral Point Spectrum ◽  
Peripheral Point

scholarly journals A note on positive semigroups

1985 ◽  
Vol 32 (3) ◽  
pp. 339-343 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Spaces ◽  
Banach Lattices ◽  
Positive Semigroups ◽  
Ordered Banach Spaces

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.

scholarly journals Strictly positive and strongly positive semigroups

1983 ◽  
Vol 34 (1) ◽  
pp. 36-48 ◽  
Author(s):  
Adam Majewski ◽  
Derek W. Robinson
Keyword(s):  
Operator Algebras ◽  
Banach Lattices ◽  
Cluster Property ◽  
Positive Semigroup ◽  
Holomorphic Semigroups ◽  
Positive Semigroups ◽  
Algebraic Setting ◽  
Strict Positivity ◽  
Invariant States ◽  
Irreducibility Criteria

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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