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1.
Interpretation, derivation and application of a variation of constants formula for measure-valued functions motivate our investigation
of properties of particular Banach spaces of Lipschitz functions on a metric space and semigroups defined on their (pre)duals.
Spaces of measures densely embed into these preduals. The metric space embeds continuously in these preduals, even isometrically
in a specific case. Under mild conditions, a semigroup of Lipschitz transformations on the metric space then embeds into a
strongly continuous semigroups of positive linear operators on these Banach spaces generated by measures.
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2.
The results provided hereby are related to the asymptotic behaviour of certain strongly continuous semigroups, which may be
expressed in terms of iterates of positive linear operators, in the sense of Altomare’s theory. We present some applications
to concrete cases involving continuous and discrete type operators, namely the Beta and the Stancu operators.
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3.
Sean T. Vittadello 《Integral Equations and Operator Theory》2009,64(4):573-597
We study representations of numerical semigroups ∑ by isometries on Hilbert space with commuting range projections. Our main
theorem says that each such representation is unitarily equivalent to the direct sum of a representation by unitaries and
a finite number of multiples of particular concrete representations by isometries. We use our main theorem to identify the
faithful representations of the C*-algebra C*(∑) generated by a universal isometric representation with commuting range projections, and also prove a structure theorem
for C*(∑).
This research was supported by the Australian Research Council. 相似文献
4.
Let be a multiplicative semigroup of positive operators on a Banach lattice E such that every is ideal-triangularizable, i.e., there is a maximal chain of closed subspaces of E that consists of closed ideals invariant under S. We consider the question under which conditions the whole semigroup is simultaneously ideal-triangularizable. In particular, we extend a recent result of G. MacDonald and H. Radjavi. We also
introduce a class of positive operators that contains all positive abstract integral operators when E is Dedekind complete.
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5.
O. Blasco M. D. Contreras S. Díaz-Madrigal J. Martínez A. G. Siskakis 《Integral Equations and Operator Theory》2008,61(1):45-62
In this paper we deal with the maximal subspace in BMOA where a general semigroup of analytic functions on the unit disk generates a strongly continuous semigroup of composition
operators. Particular cases of this question are related to a well-known theorem of Sarason about VMOA. Our results describe analytically that maximal subspace and provide a condition which is sufficient for the maximal subspace
to be exactly VMOA. A related necessary condition is also proved in the case when the semigroup has an inner Denjoy-Wolff point. As a byproduct
we provide a generalization of the theorem of Sarason.
This research has been partially supported by the Ministerio de Educación y Ciencia projects n. MTM2006-14449-C02-01 and MTM2005-08350-C03-03 and by La Consejería de Educación y Ciencia de la Junta de Andalucía. 相似文献
6.
The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy
of evolution families on the real line. We consider two general classes denoted
and
and we prove that if V,W are Banach function spaces with
and
, then the admissibility of the pair
for an evolution family
implies the uniform dichotomy of
. In addition, we consider a subclass
and we prove that if
, then the admissibility of the pair
implies the uniform exponential dichotomy of the family
. This condition becomes necessary if
. Finally, we present some applications of the main results. 相似文献
7.
P. H. Anh Ngoc S. Murakami T. Naito J. Son Shin Y. Nagabuchi 《Integral Equations and Operator Theory》2009,64(3):325-355
We first introduce the notion of positive linear Volterra-Stieltjes differential systems. Then, we give some characterizations
of positive systems. An explicit criterion and a Perron-Frobenius type theorem for positive linear Volterra-Stieltjes differential
systems are given. Next, we offer a new criterion for uniformly asymptotic stability of positive systems. Finally, we study
stability radii of positive linear Volterra-Stieltjes differential systems. It is proved that complex, real and positive stability
radius of positive linear Volterra-Stieltjes differential systems under structured perturbations coincide and can be computed
by an explicit formula. The obtained results in this paper include ones established recently for positive linear Volterra
integro-differential systems [36] and for positive linear functional differential systems [32]-[35] as particular cases. Moreover,
to the best of our knowledge, most of them are new.
The first author is supported by the Alexander von Humboldt Foundation. 相似文献
8.
A detailed study is made of matrix-valued, ordinary linear differential operators T in for 1 < p < ∞, which arise as the perturbation of a constant coefficient differential operator of order n ≥ 1 by a lower order differential operator which has a factorisation S = AB for suitable operators A and B. Via techniques from L
p
-harmonic analysis, perturbation theory and local spectral theory, it is shown that T satisfies certain local resolvent estimates, which imply the existence of local functional calculi and decomposability properties
of T.
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9.
Constantin Buşe Mihail Megan Manuela-Suzy Prajea Petre Preda 《Integral Equations and Operator Theory》2007,59(4):491-500
Among others we shall prove that an exponentially bounded evolution family U = {U(t, s)}
t≥s≥0 of bounded linear operators acting on a Banach space X is uniformly exponentially stable if and only if there exists q
[1, ∞) such that
This result seems to be new even in the finite dimensional case and it is the strong variant of an old result of E. A. Barbashin
([1]Theorem 5.1).
The first author was partially supported by the CNCSIS’s grant no. 546/2006. 相似文献
10.
We study the problem of factorisation of non-negative Fredholm operators acting in the Hilbert space L2(0, 1) and its relation to the inverse spectral problem for Bessel operators. In particular, we derive an algorithm of reconstructing
the singular potential of the Bessel operator from its spectrum and the sequence of norming constants. 相似文献
11.
Tanja Eisner 《Archiv der Mathematik》2009,92(5):451-460
We study linear operators T on Banach spaces for which there exists a C0-semigroup (T(t))t≥0 such that T = T(1). We present a necessary condition in terms of the spectral value 0 and give classes of examples for which such a C0-semigroup does or does not exist.
Received: 22 December 2008, Revised: 7 April 2009 相似文献
12.
13.
In [2] various types of closedness of subspace lattices were studied. In particular, the authors defined operator reflexivity
which can be regarded as a one-point closedness of the lattice. They asked if all subspace lattices are operator reflexive.
In this work we give an example that the answer is negative.
The second author was supported by grant no. 201/06/0128 of GA CR. 相似文献
14.
Jan Prüss 《Archiv der Mathematik》2009,92(2):158-173
Decay properties in energy norm for solutions of a class of partial differential equations with memory are studied by means
of frequency domain methods. Our results are optimal for this class, as we are able to characterize polynomial as well as exponential decay rates. The results apply to models for viscoelastic materials. An extension to a
semilinearly perturbed problem is also included.
Received: 9 July 2008, Revised: 16 September 2008 相似文献
15.
A completeness theorem is proved involving a system of integro-differential equations with some λ-depending boundary conditions.
Also some sufficient conditions for the root functions to form a Riesz basis are established.
The research was supported by the Academy of Finland (project 129092). 相似文献
16.
Hernán R. Henríquez 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(5):797-822
We establish existence of asymptotically almost periodic mild solutions for a class of semi-linear second-order abstract retarded
functional differential equations with infinite delay.
Research supported in part by FONDECYT, grant 1050314. 相似文献
17.
C. Buşe A. D. R. Choudary S. S. Dragomir M. S. Prajea 《Integral Equations and Operator Theory》2008,61(3):325-340
A result of Barbashin ([1], [15]) states that an exponentially bounded evolution family defined on a Banach space and satisfying some measurability conditions is uniformly exponentially stable if and only if for
some 1 ≤ p < ∞, we have that:
Actually the Barbashin result was formulated for non-autonomous differential equations in the framework of finite dimensional
spaces. Here we replace the above ”uniform” condition be a ”strong” one.
Among others we shall prove that the evolution family is uniformly exponentially stable if there exists a non-decreasing function with for all r > 0 such that for each , one has:
In particular, the family U is uniformly exponentially stable if and only if for some 0 < p < ∞ and each , the inequality
is fulfilled. The latter result extends a similar one from the recent paper [4]. Related results for periodic evolution families
are also obtained.
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18.
Tomas Ya. Azizov Jussi Behrndt Peter Jonas Carsten Trunk 《Integral Equations and Operator Theory》2009,63(2):151-163
For closed linear operators or relations A and B acting between Hilbert spaces and the concepts of compact and finite rank perturbations are defined with the help of the orthogonal projections P
A
and P
B
in onto the graphs of A and B. Various equivalent characterizations for such perturbations are proved and it is shown that these notions are a natural
generalization of the usual concepts of compact and finite rank perturbations.
Sadly, our colleague and friend Peter Jonas passed away on July, 18th 2007. 相似文献
19.
On a periodic boundary value problem for cyclic feedback type linear functional differential systems
Sulkhan Mukhigulashvili 《Archiv der Mathematik》2006,87(3):255-260
Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem
where ω > 0, ℓi : C([0, ω])→ L([0,ω]) are linear bounded operators, and qi∈L([0, ω]).
Received: 11 June 2005 相似文献
20.
The classification of the fully invariant subgroups of a reduced Abelian p-group is a difficult long-standing problem when one moves outside of the class of fully transitive groups. In this work we
restrict attention to the socles of fully invariant subgroups and introduce a new class of groups which we term socle-regular groups; this class is shown to be large and strictly contains the class of fully transitive groups. The basic properties of such
groups are investigated but it is shown that the classification of even this simplified class of groups, seems extremely difficult.
Received: 4 September 2008 相似文献