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1.
《Arkiv f?r Matematik》1992,30(1):217-220
We determine the smallest Schatten class containing all integral operators with kernels inL
p(Lp', q)symm, where 2 <p∞ and 1≦q≦∞. In particular, we give a negative answer to a problem posed by Arazy, Fisher, Janson and Peetre in [1].
Supported in part by DGICYT (SAB-90-0033). 相似文献
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We study a system of differential equations in Schatten classes of operators, ${\mathcal{C}_p(\mathcal{H})\,(1 \leq p < \infty}$ ), with ${\mathcal{H}}$ a separable complex Hilbert space. The systems considered are infinite dimensional generalizations of mathematical models of unsupervised learning. In this new setting, we address the usual questions of existence and uniqueness of solutions. Under some restrictions on the spectral properties of the initial conditions, we explicitly solve the system. We also discuss the long-term behavior of solutions. 相似文献
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We address the problem of determining membership in Schatten-Von Neumann ideals S p of integration operators (T g f)(z) = ∫ 0 z = ∫ 0 z f(ξ)g′(ξ)dξ acting on Dirichlet type spaces. We also study this problem for multiplication, Hankel and Toeplitz operators. In particular, we provide an extension of Luecking's result on Toeplitz operators [10, p. 347]. 相似文献
6.
Matthew M. Jones 《Proceedings of the American Mathematical Society》2006,134(7):1947-1953
We provide a direct construction of the mapping given by Tom Carroll and Carl Cowen in `Compact composition operators not in the Schatten classes' (1991, in J. Operator Theory 26).
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We study composition operators, induced by a sub-domain of the unit disc whose boundary intersects the unit circle at 1 and which has, in a neighborhood of 1, a polar equation 1−r=γ(|θ|) (see Fig. 1). We obtain an explicit characterization for the membership in Schatten p-classes, in terms of γ. 相似文献
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We prove that if ω, ω1, ω2, v1, v2 are appropriate, , j=1,2, and ωa∈Lp, then the Toeplitz operator Tph1,h2(a) from to belongs to the Schatten-von Neumann class of order p. From this property we prove convolution properties between weighted Lebesgue spaces and Schatten-von Neumann classes of symbols in pseudo-differential calculus. 相似文献
9.
Roshdi Khalil 《Journal of Functional Analysis》1982,47(3):305-313
Let Cp be the class of all compact operators A on the Hilbert space l2 for which , where {λi} is the eigen values of . The object of this paper is to prove some results concerning the Schur multipliers of Cp. 相似文献
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Liliana Gabriela Gheorghe 《Annali di Matematica Pura ed Applicata》2001,180(2):203-210
We study membership to Schatten ideals S
E
, associated with a monotone Riesz–Fischer space E, for the Hankel operators H
f
defined on the Hardy space H
2(∂D). The conditions are expressed in terms of regularity of its symbol: we prove that H
f
∈S
E
if and only if f∈B
E
, the Besov space associated with a monotone Riesz–Fischer space E(dλ) over the measure space (D,dλ) and the main tool is the interpolation of operators.
Received: December 17, 1999; in final form: September 25, 2000?Published online: July 13, 2001 相似文献
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Minghua Lin 《Comptes Rendus Mathematique》2018,356(5):517-522
Michael Gil' recently obtained some bounds for eigenvalues in [J. Funct. Anal. 267 (2014) 3500–3506] and [Commun. Contemp. Math. 18 (2016) 1550022], which improve some classical results related to this aspect. We revisit these results by providing genuinely different arguments (e.g., using Aluthge transform, majorization). New results are derived along our discussions. 相似文献
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Hyponormality, normality and subnormality for unbounded operators on Hilbert space are investigated and quasi- similarity of such operators is discussed. 相似文献
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O. Guédon G. Paouris 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(1):87
Let 1?p?∞ and be the unit ball of the Schatten trace class of matrices on Cn or on Rn, normalized to have Lebesgue measure equal to one. We prove that
17.
Elena Cordero Karlheinz Grö chenig 《Proceedings of the American Mathematical Society》2005,133(12):3573-3579
We study time-frequency localization operators of the form , where is the symbol of the operator and are the analysis and synthesis windows, respectively. It is shown in an earlier paper by the authors that a sufficient condition for , the Schatten class of order , is that belongs to the modulation space and the window functions to the modulation space . Here we prove a partial converse: if for every pair of window functions with a uniform norm estimate, then the corresponding symbol must belong to the modulation space . In this sense, modulation spaces are optimal for the study of localization operators. The main ingredients in our proofs are frame theory and Gabor frames. For and , we recapture earlier results, which were obtained by different methods.
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We study relations between Schatten classes and product operator ideals, where one of the factors is the Banach ideal ΠE,2 of (E, 2)‐summing operators, and where E is a Banach sequence space with ?2 ? E. We show that for a large class of 2‐convex symmetric Banach sequence spaces the product ideal ΠE,2 ○ ??aq,s is an extension of the Schatten class ??F with a suitable Lorentz space F. As an application, we obtain that if 2 ≤ p, q < ∞, 1/r = 1/p + 1/q and E is a 2‐convex symmetric space with fundamental function λE(n) ≈? n1/p, then ΠE,2 ○ Πq is an extension of the Schatten class ??r,q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Fabrizio Colombo Jonathan Gantner Tim Janssens 《Mathematical Methods in the Applied Sciences》2016,39(18):5582-5606
In this paper, we introduce the Schatten class and the Berezin transform of quaternionic operators. The first topic is of great importance in operator theory, but it is also necessary to study the second one, which requires the notion of trace class operators, a particular case of the Schatten class. Regarding the Berezin transform, we give the general definition and properties. Then we concentrate on the setting of weighted Bergman spaces of slice hyperholomorphic functions. Our results are based on the S‐spectrum of quaternionic operators, which is the notion of spectrum that appears in the quaternionic version of the spectral theorem and in the quaternionic S‐functional calculus. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献