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1.
Suppose 1≤p,q≤∞ and α > (1/p−1/q)+. Then we investigate compactness properties of the integral operator when regarded as operator from Lp[0,1] into Lq[0,1]. We prove that its Kolmogorov numbers tend to zero faster than exp(−cαn1/2). This extends former results of Laptev in the case p=q=2 and of the authors for p=2 and q=∞. As application we investigate compactness properties of related integral operators as, for example, of the difference
between the fractional integration operators of Riemann–Liouville and Weyl type. It is shown that both types of fractional
integration operators possess the same degree of compactness. In some cases this allows to determine the strong asymptotic
behavior of the Kolmogorov numbers of Riemann–Liouville operators.
In memoria of Eduard (University of the West Indies) who passed away in October 2004. 相似文献
2.
José Giménez 《Integral Equations and Operator Theory》2002,43(4):385-396
We study joint hyponormality and joint subnormality of ofn-tuples of commuting composition operators with linear fractional symbols, acting on the Hardy spaceH
2. We also consider subnormality ofn-tuples of adjoints of composition operators. 相似文献
3.
We study two semigroups
of operators between Banach spaces, related with the finite representability ofc
0 and ℓ1. We show that these semigroups are open, have nice duality properties and can be characterized in terms of compact perturbations,
and in terms of the properties of their ultrapowers. We obtain analogous results for their associated dual semigroups.
Supported in part by DGICYT Grant PB 94-1052 (Spain).
Supported by a postdoctoral Grant of the Ministry of Spain for Education and Science 相似文献
4.
Let B(H) denote the algebra of operators on a complex separable
Hilbert space H, and let A $\in$ B(H) have the polar decomposition A = U|A|.
The Aluthge transform
is defined to be the operator
.
We say that A $\in$ B(H) is p-hyponormal,
.
Let
.
Given p-hyponormal
, such that AB is compact, this
note considers the relationship between
denotes an enumeration in decreasing order repeated according
to multiplicity of the eigenvalues of the
compact operator T (respectively,
singular values of the compact operator T).
It is proved that
is bounded above by
and below by
for all j = 1, 2, . . .
and that if also
is normal, then there exists a unitary
U1 such that
for all j = 1, 2, . . .. 相似文献
5.
The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
6.
The Weiss conjecture on admissibility of observation operators for contraction semigroups 总被引:4,自引:0,他引:4
We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functionalC is infinite-time admissible if and only if there is anM>0 such that
for alls in the open right half-plane. HereA denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators. 相似文献
7.
M.S. Moslehian 《Linear algebra and its applications》2009,430(4):1131-1987
We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is equivalent to operator convexity of given continuous real function. 相似文献
8.
José E. Galé Pedro J. Miana Detlef Müller 《Integral Equations and Operator Theory》2007,57(3):327-337
We consider some extensions of well-boundedness and Cm-scalarity by using fractional calculus, and prove some theorems accordingly. These results are applied to the usual Laplacian
on Rn and sub-Laplacians on nilpotent Lie groups.
The research of first and second authors has been partly supported by the Project MTM2004-03036 of the M.C.YT.-DGI/F.E.D.E.R.,
Spain, and the Project E-12/25, D. G. Aragón, Spain. Part of the research of second author was developed in the Christian-Albrechts
Universit?t in Kiel, while he was enjoying a HARP-postdoctoral position in the European Harmonic Analysis Network, HARP, IHP
2002-06. 相似文献
9.
A compactness criterion and application to the commutators associated with Schrödinger operators 下载免费PDF全文
Let T be an integral operator. In this paper, we introduce a ‐compactness criterion of , where . As an application, we apply this criterion to deal with ‐compactness of commutators associated to Schrödinger operators with potentials in the reverse Hölder's class. 相似文献
10.
11.
12.
We shall discuss geometric properties of a quadrangle with parallelogramic properties in a convex cone of positive definite matrices with respect to Thompson metric. 相似文献
13.
《Mathematische Nachrichten》2017,290(11-12):1663-1677
We investigate interpolation properties of compact bilinear operators under the general real method. Results apply in particular to the real method with a function parameter and also to the complex method in the special case when the couple in the target reduces to a single Banach space or the source is a product of two fixed Banach spaces. 相似文献
14.
Daniel Alpay Piet Bruinsma Aad Dijksma Henk de Snoo 《Integral Equations and Operator Theory》1992,15(3):378-388
By an oversight on the part of the authors this section was not included in the paper previously published in Integral Equations Operator Theory, volume 14/4 (1991), 466–500.
Present address:Department of Mathematics Ben-Gurion University of the Negev Beersheva Israel 相似文献
15.
W. V. Smith 《Periodica Mathematica Hungarica》1982,13(4):273-287
We continue the development of part I. The Riesz representation theorem is proved without assuming local convexity. This theorem is applied to give sufficient conditions for an operator (continuous or otherwise) to be spectral. A uniqueness problem is pointed out and the function calculus is extended to the case of several variables. A Radon—Nikodym theorem is proved. 相似文献
16.
Let be a densely defined operator on a Banach space X. Characterizations of when generates a C0‐semigroup on X are known. The famous result of Lumer and Phillips states that it is so if and only if is dissipative and is dense in X for some . There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kamińska provides perturbation criteria of dissipative operators in terms of ergodic properties. These results, and others, are shown to remain valid in the setting of general non–normable locally convex spaces. Applications of the results to concrete examples of operators on function spaces are also presented. 相似文献
17.
We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces. 相似文献
18.
19.
Daniel Simson 《Linear algebra and its applications》2010,433(4):699-717
Linear algebra technique in the study of linear representations of finite posets is developed in the paper. A concept of a quadratic wandering on a class of posets I is introduced and finite posets I are studied by means of the four integral bilinear forms (1.1), the associated Coxeter transformations, and the Coxeter polynomials (in connection with bilinear forms of Dynkin diagrams, extended Dynkin diagrams and irreducible root systems are also studied). Bilinear equivalences between some of the forms are established and equivalences with the bilinear forms of Dynkin diagrams and extended Dynkin diagrams are discussed. A homological interpretation of the bilinear forms (1.1) is given and Z-bilinear equivalences between them are discussed. By applying well-known results of Bongartz, Loupias, and Zavadskij-Shkabara, we give several characterisations of posets I, with the Euler form weakly positive (resp. with the reduced Euler form weakly positive), and posets I, with the Tits form weakly positive. 相似文献
20.
We consider hypercyclic composition operators on
which can be obtained from the translation operator using polynomial automorphisms of
. In particular we show that if C
S
is a hypercyclic operator for an affine automorphism S on
, then
for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic
functions on ℓ1.
Received: 8 June 2006 Revised: 26 September 2006 相似文献