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1.
V. I. Ovchinnikov 《Mathematical Notes》1998,63(6):764-769
In this paper it is proved that the ideal of trace-class operators acting in a couple of Hilbert spaces coincides with the ideal of coherent trace-class operators. A new formula is derived for theK-functional in the couple of algebras of all bounded linear operators acting in a Hilbert couple, and new interpolation theorems are proved for trace class operators.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 866–872, June, 1998.This research was partially supported by the International Science Foundation and the Russian Government under grant JD 7100. 相似文献
2.
N. é. Mikhailovskii 《Mathematical Notes》1998,63(1):72-83
Asymptotic estimates of the form mrA = O(InN · ln
d
ɛ
−1), whered is the dimension of the initial space, for mosaic ranks of discrete analog of Calderón-Zygmund operators are obtained for
various mosaic covers.
Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 81–94, January, 1998. 相似文献
3.
A theorem on interpolation of bilinear operators in symmetric Marcinkiewicz spaces is proved. It follows from the general
bilinear results for the Peetre and Peetre-Gustavsson interpolation functors.
Translated fromMatematicheskie Zametki, Vol. 60, No. 4, pp. 483–494, October, 1996. 相似文献
4.
Yu. A. Konyaev 《Mathematical Notes》1997,62(4):414-419
A class of singularly perturbed initial and boundary value problems for systems of linear differential equations with singularities
of various types is studied. The asymptotics of the solutions of these problems is constructed; in contrast to known results,
it involves boundary layers of new types that are dependent not only on the spectrum of the limit operator.
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 494–501, October, 1997.
Translated by N. K. Kulman 相似文献
5.
Shanti Prasanna 《Proceedings Mathematical Sciences》1982,91(1):59-63
Using the notion of thin sets we prove a theorem of Weyl type for the Wolf essential spectrum ofT ∈β (H). *Further we show that Weyl’s theorem holds for a restriction convexoid operator and consequently modify some results of
Berberian. Finally we show that Weyl’s theorem holds for a paranormal operator and that a polynomially compact paranormal
operator is a compact perturbation of a diagnoal normal operator. A structure theorem for polynomially compact paranormal
operators is also given. 相似文献
6.
B. Vainberg & Marc Durand 《Applicable analysis》2013,92(8):821-838
Out problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto-acoustic operator H defined in ?2 × I where I is a bounded interval of ? with coefficients depending only on z ∈ I. The “conjugate operator method” will be applied to an operator obtained by a spectral decomposition of the partial Fourier transform ? of H. Around each value of the spectrum (except the eigenvalues) including the thresholds, a conjugate operator is constructed which permits to get the ”good properties“ of regularity for H. A limiting absorption principle is then obtained for a large class of operators at every point of the spectrum (except eigenvalues). 相似文献
7.
Herrero’s conjecture that each operator with connected spectrum acting on complex, separable Hilbert space can be written
as the sum of a strongly irreducible operator and a compact operator is proved.
Jiang, C. L., Power, S., Wang, Z. Y., Biquasitriangular + small compact = strongly irreducible,J. London Math., to be published. 相似文献
8.
Viorel Catană 《Applicable analysis》2013,92(6):657-666
Following Wong's point of view, we construct the minimal and maximal extension in Lp (? n ), 1 < p < ∞ for M-hypoelliptic pseudo-differential operators, which have been introduced and studied by Garello and Morando. We give some facts about the domain of minimal and maximal extensions of M-hypoelliptic pseudo-differential operators. For M-hypoelliptic pseudo-differential operators with constant coefficients, the spectrum and essential spectrum are computed. 相似文献
9.
We study properties of Jordan representations ofH-dissipative operators in a finite-dimensional indefiniteH-space. An algebraic proof is given of the fact that such operators always have maximal semidefinite invariant subspaces.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 163–169, February, 1998.
The authors axe grateful to Professor A. A. Shkalikov for useful discussions.
The research of the first author was supported by INTAS under grant No. 93-0249. The research of the second author was supported
by the International Science Foundation and the Russian Government under grant No. NZP300. 相似文献
10.
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
11.
LetL(X, Y) be the Banach space of all continuous linear operators fromX toY, and letK(X, Y) be the subspace of compact operators. Some versions of the classical Pitt theorem (ifp>q, thenK(l
p, lq)=L(lp, lq)) for subspaces of Lorentz and Orlicz sequence spaces are established.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 18–25, January, 1997.
Translated by V. N. Dubrovsky 相似文献
12.
V. A. Sloushch 《Journal of Mathematical Sciences》2000,101(3):3190-3192
Let A be a self-adjoint operator, let (α,β) be a gap in the spectrum of A, and let B=A+V, where, in general, the perturbation
operator V is unbounded. We establish some abstract conditions under which the spectrum of B in (α,β) is discrete; does not
accumulate to β; is finite. An estimate of the number of eigenvalues of B in (α,β) is obtained. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 237–241.
Translated by S. V. Kislyakov. 相似文献
13.
V. I. Derguzov 《Journal of Mathematical Sciences》1995,77(4):3295-3302
A waveguide operator is defined. It is proved that its spectrum coincides with the spectrum of a lightguide. The classification
of singular points of the continuous spectrum is given. Invariant subspaces of the waveguide operator are distinguished that
are related to an interval of the continuous spectrum without singular points. Bibliography: 9 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 14, 1995, pp. 51–62. 相似文献
14.
V. S. Yarunin 《Journal of Mathematical Sciences》1998,88(2):313-317
The two-branch spectrum of excitations of a weakly nonideal Bose-gas is obtained by using the integral over trajectories in
the canonical ensemble with constraint. A rearrangment of the spectrum at the condensate density providing equilibrium of
the attractive and repulsive forces in the interatomic potential is discovered. The influence of the quantum bosonic oscillations
in the ground state on the stability of the branches is investigated. Bibliography: 5 titles.
Dedicated to the memory of V. N. Popov
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 224, 1994, pp. 310–317.
Translated by B. Bekker. 相似文献
15.
For an integer k ≥ 2, kth‐order slant Toeplitz operator Uφ [1] with symbol φ in L∞(??), where ?? is the unit circle in the complex plane, is an operator whose representing matrixM = (αij ) is given by αij = 〈φ, zki–j〉, where 〈. , .〉 is the usual inner product in L2(??). The operator Vφ denotes the compression of Uφ to H2(??) (Hardy space). Algebraic and spectral properties of the operator Vφ are discussed. It is proved that spectral radius of Vφ equals the spectral radius of Uφ, if φ is analytic or co‐analytic, and if Tφ is invertible then the spectrum of Vφ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
In this paper we are concerned with the complete spectral analysis for the operator 𝒯 = 𝒳𝒮𝒰 in the space Lp(𝕋) (𝕋 denoting the unit circle), where 𝒳 is the characteristic function of some arc of 𝕋, 𝒮 is the singular integral operator with Cauchy kernel and 𝒰 is a Carleman shift operator which satisfies the relations 𝒰2 = I and 𝒮𝒰 = ±𝒰𝒮, where the sign + or — is taken in dependence on whether 𝒰 is a shift operator on Lp(𝕋) preserving or changing the orientation of 𝕋. This includes the identification of the Fredholm and essential parts of the spectrum of the operator 𝒯, the determination of the defect numbers of 𝒯 — λI, for λ in the Fredholm part of the spectrum, as well as a formula for the resolvent operator. 相似文献
17.
V. M. Manuilov 《Mathematical Notes》1997,62(6):726-730
The classical Hilbert-Schmidt theorem can be extended to compact operators on HilbertA-modules overW
*-algebras of finite type; i.e., with minor restrictions, compact operators onH*
A
can be diagonalized overA. We show that ifB is a weakly denseC
*-subalgebra ofA with real rank zero and if some additional condition holds, then the natural extension fromH
B
toH*
A
⊃H
B
of a compact operator can be diagonalized so that the diagonal elements belong to the originalC
*-algebraB.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 865–870, December, 1997.
Translated by O. V. Sipacheva 相似文献
18.
V. D. Lyakhovskii 《Journal of Mathematical Sciences》1997,83(1):106-112
A wide class of quantum universal enveloping algebras uniquely corresponding to Hopf algebras H with spectrum Q(H) in the
category of groups is defined. Such quantum algebras are the quantum groups of the simply connected solvable Lie groups P(H).
Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 168–178
Translated by V. D. Lyakhovskii 相似文献
19.
Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Σn δ ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
M. I. Gil' 《Proceedings of the American Mathematical Society》2003,131(12):3737-3746
A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.