共查询到20条相似文献,搜索用时 15 毫秒
1.
Linear time-varying Volterra integro-differential equations of non-convolution type are considered. Positivity is characterized
and a sufficient condition for exponential asymptotic stability is presented.
The second author thanks the Alexander von Humboldt Foundation for their support. 相似文献
The second author thanks the Alexander von Humboldt Foundation for their support. 相似文献
2.
Roman Drnovsek 《Proceedings of the American Mathematical Society》2007,135(12):3833-3836
Let be a positive operator on a complex Banach lattice. We prove that is greater than or equal to the identity operator if
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Witold Wnuk 《Positivity》2013,17(3):759-773
The paper contains several characterizations of Banach lattices $E$ with the dual positive Schur property (i.e., $0 \le f_n \xrightarrow {\sigma (E^*,E)} 0$ implies $\Vert f_n\Vert \rightarrow 0$ ) and various examples of spaces having this property. We also investigate relationships between the dual positive Schur property, the positive Schur property, the positive Grothendieck property and the weak Dunford–Pettis property. 相似文献
5.
In this paper, we study the stability radii of positive linear systems with delays with respect to various classes of perturbations in infinite dimensional spaces. It is shown that the positive, real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by a simple example. 相似文献
6.
Zhang Xiao-Dong 《Indagationes Mathematicae》1996,7(4):559
Extension properties of compact positive operators on Banach lattices are investigated. The following results are obtained:
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(1) Any compact positive operator (any compact lattice homomorphism, resp.) from a majorizing sublattice G of a Banach lattice E into another Banach lattice F can be extended to a compact positive operator (a compact lattice homomorphism, resp.) from E into F; 2.
(2) Any compact positive operator defined on a closed majorizing sublattice G of a Banach lattice E has a compact positive extension on E that preserves the spectrum (a necessary modification is needed).
7.
Mohammed Taghi Jahandideh 《Proceedings of the American Mathematical Society》1997,125(9):2661-2670
There are some known results that guarantee the existence of a nontrivial closed invariant ideal for a quasinilpotent positive operator on an -space with unit or a Banach lattice whose positive cone contains an extreme ray. Some recent results also guarantee the existence of such ideals for certain positive operators, e.g. a compact quasinilpotent positive operator, on an arbitrary Banach lattice. The main object of this article is to use these results in constructing a maximal closed ideal chain, each of whose members is invariant under a certain collection of operators that are related to compact positive operators, or to quasinilpotent positive operators.
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In this paper we derive existence and comparison results for discontinuous improper functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. For this purpose we prove Dominated and Monotone Convergence Theorems for improper integrals. The obtained results are then applied to first-order impulsive differential equations. Concrete examples are also solved by using symbolic programming. 相似文献
10.
Bui The Anh 《Positivity》2010,14(1):181-189
This paper considers the asymptotic behaviour of a finite-dimensional positive linear Volterra equation with delays. The main results give conditions which ensure that the exact rate of decay of the solution can be determined. 相似文献
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Egotanda Dieudonné 《Journal of Mathematical Analysis and Applications》2003,279(2):756-767
In this paper we extend M. Lin's definition of mixing for positive contractions in L1(X,Σ,m) with m(X)=1 to positive operators in Banach lattices with weak-order units, and we generalize Lin's Theorem 2.1 (Z. Wahrsch. Verw. Gebiete 19 (1971) 231-249) to the case of power-bounded positive operators in KB-spaces. In the particular case of weakly compact power-bounded positive operators, the same theorem is extended to Banach lattices with order-continuous norms. 相似文献
13.
N. J. Nielsen 《Israel Journal of Mathematics》1988,62(1):99-112
In this paper we study the positive approximation property (p.a.p.) of Banach lattices. The main results give some characterizations
of the p.a.p. and the bounded p.a.p. Some perturbation results on positive operators, which are of interest in other contexts,
too, are proved. 相似文献
14.
Marek Wójtowicz 《Positivity》2013,17(2):257-263
Let X be a Banach lattice, and let ${x\in X{\setminus}\{0\}}$ . We study the structure of the set Grad(x), of all supporting functionals of x. If X is a Dedekind σ-complete Banach lattice, there is an isometry from Grad(x) onto Grad(|x|); hence the elements x and |x| are smooth simultaneously. And if, additionally, X* is strictly monotone then Grad(|x|) consists of positive functionals. As a by-product of our results we obtain that an arbitrary Banach lattice X is strictly monotone whenever its dual X* is smooth. 相似文献
15.
Belmesnaoui Aqzzouz Redouane Nouira Larbi Zraoula 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):287-294
We give some sufficient and necessary conditions for that a positive Dunford-Pettis operator admits a dual operator which
is also Dunford-Pettis, and conversely.
相似文献
16.
Liping Wen Yuexin Yu Shoufu Li 《Journal of Computational and Applied Mathematics》2009,230(2):351-359
This paper is concerned with the stability and asymptotic stability of θ-methods for the initial value problems of nonlinear stiff Volterra functional differential equations in Banach spaces. A series of new stability and asymptotic stability results of θ-methods are obtained. 相似文献
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Belmesnaoui Aqzzouz Redouane Nouira Larbi Zraoula 《Journal of Mathematical Analysis and Applications》2006,324(1):49-59
We give several characterizations of Banach lattices on which each positive Dunford-Pettis operator is compact. As consequences, we obtain new sufficient and necessary conditions under which a norm of a Banach lattice is order continuous, a positive weakly compact operator is compact and the dual operator of a positive Dunford-Pettis operator is Dunford-Pettis. 相似文献
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This paper is the first systematic study of homogeneous polynomials on Banach lattices. A variety of new Banach spaces and Banach lattices of multilinear maps, homogeneous polynomials, and operators are introduced. The main technique is to employ positive tensor products and quotients of positive tensor products. Our theorems generalize the results on orthogonally additive polynomials by Benyamini, Lassalle, and Llavona (2006) in [4], the results by Grecu and Ryan (2005) in [14], and the results by Sundaresan (1991) in [23]. 相似文献