Generators of positive semigroups

1984 ◽  
pp. 1-15 ◽  
Author(s):  
W. Arendt
Keyword(s):  
Positive Semigroups

Perturbations of positive semigroups on $$L_p$$ L p -spaces

Positivity ◽  
2015 ◽  
Vol 20 (2) ◽  
pp. 467-481
Author(s):  
Christian Seifert ◽  
Marcus Waurick
Keyword(s):  
Positive Semigroups

Hadamard Completely Positive Semigroups

2019 ◽  
Vol 26 (04) ◽  
pp. 1950020
Author(s):  
Fabio Benatti
Keyword(s):  
Continuous Semigroup ◽  
Hadamard Product ◽  
Product Rule ◽  
Density Matrices ◽  
Completely Positive ◽  
Positive Semigroups ◽  
Completely Positive Semigroups

We review the Gorini, Kossakowski, Sudarshan derivation of the generator of a completely positive norm-continuous semigroup when the constituent maps act on density matrices according to the Hadamard product rule.

Boundary conditions for one-dimensional positive semigroups

1992 ◽  
Vol 45 (1) ◽  
pp. 92-119 ◽  
Author(s):  
Marlene G. Ulmet
Keyword(s):  
Boundary Conditions ◽  
One Dimensional ◽  
Positive Semigroups

Asymptotic behaviour of positive semigroups

1987 ◽  
Vol 195 (4) ◽  
pp. 481-485 ◽  
Author(s):  
Tilman Schanbacher
Keyword(s):  
Asymptotic Behaviour ◽  
Positive Semigroups

scholarly journals Lifting Fixed Points of Completely Positive Semigroups

2011 ◽  
Vol 72 (2) ◽  
pp. 219-222
Author(s):  
Bebe Prunaru
Keyword(s):  
Fixed Points ◽  
Completely Positive ◽  
Positive Semigroups ◽  
Completely Positive Semigroups

scholarly journals ON THE INDEX AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS

1999 ◽  
Vol 10 (07) ◽  
pp. 791-823 ◽  
Author(s):  
WILLIAM ARVESON
Keyword(s):  
Bounded Operator ◽  
Positive Semigroup ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Positive Semigroups ◽  
Matrix Algebras ◽  
Positive Maps ◽  
Completely Positive Semigroups ◽  
Numerical Index ◽  
Completely Positive Semigroup

It is known that every semigroup of normal completely positive maps P = {Pt:t≥ 0} of ℬ(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0 acting on ℬ(K) for some Hilbert space K⊇H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the index of P agrees with the index of its minimal dilation to an E0-semigroup. However, no examples were discussed, and no computations were made. In this paper we calculate the index of a unital completely positive semigroup whose generator is a bounded operator [Formula: see text] in terms of natural structures associated with the generator. This includes all unital CP semigroups acting on matrix algebras. We also show that the minimal dilation of the semigroup P={ exp tL:t≥ 0} to an E0-semigroup is is cocycle conjugate to a CAR/CCR flow.

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

Perturbations of positive semigroups and applications to population genetics

1988 ◽  
Vol 197 (2) ◽  
pp. 259-272 ◽  
Author(s):  
Reinhard B�rger
Keyword(s):  
Population Genetics ◽  
Positive Semigroups

scholarly journals Positive semigroups and abstract Lyapunov equations

Positivity ◽  
2014 ◽  
Vol 19 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Sergiy Koshkin
Keyword(s):  
Lyapunov Equations ◽  
Positive Semigroups
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