On resolvent positive operators and positive C0-semigroups on AL-spaces.
On some ergodic properties for continuous and affine functions
Two problems posed by Choquet and Foias are solved:(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such thatfor each in , but does not converge to 0.
On the class of b-L-weakly and order M-weakly compact operators
In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
On the class of order almost L-weakly compact operators
We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.
On the class of order Dunford-Pettis operators
We characterize Banach lattices and on which the adjoint of each operator from into which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if and are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator from into has an adjoint Dunford-Pettis operator from into if, and only if, the norm of is order continuous or has the Schur property. As a consequence we show that, if and are two Banach...
On the computation of some quantities in the theory of Fredholm operators
On the ergodic power function for invertible positive operators
On the essential order spectrum
On the lattice structure of invariant functions for Markov operators on
On the local spectral radius in partially ordered Banach spaces
On the modulus of one-parameter semigroups.
On the o-Spectrum of Order Bounded Operators.
On the o-Spektrum of Regular Operators and the Spectrum of Measures.
On the partial ordering of almost definite matrices
On the Perron-Frobenius theory for sets of positive operators
On the positivity of the unit element in a normed lattice ordered algebra
On the stability of strongly continuous semigroups of positive operators on
On the Structure of Non-Weakly Compact Operators on Banach Lattices.
On Theorems of de Pagter and Ando-Krieger.
Open partial isometries and positivity in operator spaces
We first study positivity in C*-modules using tripotents ( = partial isometries) which are what we call open. This is then used to study ordered operator spaces via an "ordered noncommutative Shilov boundary" which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the arrows completely positive. Because of their independent interest, we also systematically study open tripotents and their properties.