Characterization of positive semigroups on banach lattices

1986 ◽  
pp. 247-291 ◽  
Author(s):  
Wolfgang Arendt
Keyword(s):  
Banach Lattices ◽  
Positive Semigroups

scholarly journals A characterization of discrete Banach lattices with order continuous norms

1988 ◽  
Vol 104 (1) ◽  
pp. 197-197 ◽  
Author(s):  
Witold Wnuk
Keyword(s):  
Banach Lattices ◽  
Order Continuous

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.

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

A characterization of weakly sequentially complete Banach lattices

1985 ◽  
Vol 190 (3) ◽  
pp. 379-385 ◽  
Author(s):  
V. Caselles
Keyword(s):  
Banach Lattices

scholarly journals Cone characterization of reflexive Banach lattices

1995 ◽  
Vol 37 (1) ◽  
pp. 65-67 ◽  
Author(s):  
Ioannis A. Polyrakis
Keyword(s):  
Banach Lattice ◽  
Normal Cone ◽  
Banach Lattices

AbstractWe prove that a Banach lattice X is reflexive if and only if X+ does not contain a closed normal cone with an unbounded closed dentable base.

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

Interpolation of weighted Banach lattices. A characterization of relatively decomposable Banach lattices

2003 ◽  
Vol 165 (787) ◽  
pp. 0-0 ◽  
Author(s):  
Michael Cwikel ◽  
Per G. Nilsson ◽  
Gideon Schechtman
Keyword(s):  
Banach Lattices

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.

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