共查询到20条相似文献,搜索用时 0 毫秒
1.
Asao Arai 《Integral Equations and Operator Theory》1993,17(4):451-463
A new characterization of anticommutativity of (unbounded) self-adjoint operators is presented in connection with Clifford algebra. Some consequences of the characterization and applications are discussed. 相似文献
2.
Sergio Albeverio Alexei Konstantinov Volodymyr Koshmanenko 《Integral Equations and Operator Theory》2005,52(4):455-464
The decomposition theory for the singular continuous spectrum of rank one singular perturbations is studied. A generalization of the well-known Aronszajn-Donoghue theory to the case of decompositions with respect to α-dimensional Hausdorff measures is given and a characterization of the supports of the α-singular, α-absolutely continuous, and strongly α-continuous parts of the spectral measure of
- class rank one singular perturbations is given in terms of the limiting behaviour of the regularized Borel transform. 相似文献
3.
Michał Wojtylak 《Integral Equations and Operator Theory》2007,59(1):129-147
The commutators of 2 × 2 block operator matrices with (unbounded) operator entries are investigated. The matrix representation
of a symmetric operator in a Krein space is exploited. As a consequence, the domination result due to Cichoń, Stochel and
Szafraniec is extended to the case of Krein spaces. 相似文献
4.
5.
Pavel Exner Takashi Ichinose Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2007,57(1):67-81
We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator.
Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive
assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the
situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies. 相似文献
6.
7.
Željko Čučković 《Integral Equations and Operator Theory》2007,59(3):345-353
We study finite rank perturbations of the Brown-Halmos type results involving products of Toeplitz operators acting on the
Bergman space.
相似文献
8.
The aim of this paper is to prove two perturbation results for a selfadjoint operator A in a Krein space
which can roughly be described as follows: (1) If is an open subset of
and all spectral subspaces for A corresponding to compact subsets of have finite rank of negativity, the same is true for a selfadjoint operator B in
for which the difference of the resolvents of A and B is compact. (2) The property that there exists some neighbourhood of such that the restriction of A to a spectral subspace for A corresponding to is a nonnegative operator in
is preserved under relative
perturbations in form sense if the resulting operator is again selfadjoint. The assertion (1) is proved for selfadjoint relations A and B. (1) and (2) generalize some known results. 相似文献
9.
Asao Arai 《Integral Equations and Operator Theory》1993,16(1):38-63
LetA andB be anticommuting self-adjoint operators in a Hilbert space . It is proven thatiAB is essentially self-adjoint on a suitable domain and its closureC(A, B) anticommutes withA andB. LetU
s
be the partial isometry associated with the self-adjoint operatorsS, i.e., the partial isometry defined by the polar decompositionS=U
S
|S|. LetP
S
be the orthogonal projection onto (KerS). Then the following are proven: (i) The operatorsU
A
,U
B
,U
C(A,B)
,P
A
,P
B
, andP
A
P
B
multiplied by some constants satisfy a set of commutation relations, which may be regarded as an extension of that satisfied by the standard basis of the Lie algebra
of the special unitary groupSU(2); (ii) There exists a Lie algebra
associated with those operators; (iii) If is separable andA andB are injective, then
gives a completely reducible representation of
with each irreducible component being the spin representation of the Clifford algebra associated with 3; This result can be extended to the case whereA andB are not necessarily injective. Moreover, some properties ofA+B are discussed. The abstract results are applied to Dirac operators. 相似文献
10.
Asao Arai 《Integral Equations and Operator Theory》1995,21(2):139-173
LetA andB be two anticommuting self-adjoint operators andV() be a symmetric operator in a Hilbert space, where >0 is a parameter. It is proven that, under some conditions forV(), the resolvents of A+2
B±2|B|+V() converge as . Applications to the nonrelativistic-limit problem of Dirac operators and supersymmetry are discussed.This work is supported by the Grant-In-Aid 0560139 for science research from the Ministry of Education, Japan. 相似文献
11.
12.
This paper studies the class of pure hyponormal operators with
rank one self-commutator satisfying the condition that their spectra are quadrature
domains. 相似文献
13.
Heinz Langer Matthias Langer Alexander Markus Christiane Tretter 《Complex Analysis and Operator Theory》2008,2(1):99-134
We establish sufficient conditions for the so-called Virozub–Matsaev condition for twice continuously differentiable self-adjoint
operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive
type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.
Received: September 22, 2007. Accepted: September 29, 2007. 相似文献
14.
15.
It is well known that continuous bilinear forms on C(K) × C(K) are 2-dominated. This paper shows that generalizations of this result are not to be expected. The main result asserts that for every
-space E(1 p ), every n 2, every r > 0 and every Banach space F , there exists an n-homogeneous polynomial P : E F such that P is not of type [r], hence P is neither r-dominated nor r-semi-integral (if n = 2 and p = , F is supposed to contain an isomorphic copy of some
, 1q < ).Received: 24 November 2003 相似文献
16.
Rank one perturbations of selfadjoint operators which are not necessarily semibounded are studied in the present paper. It is proven that such perturbations are uniquely defined, if they are bounded in the sense of forms. We also show that form unbounded rank one perturbations can be uniquely defined if the original operator and the perturbation are homogeneous with respect to a certain one parameter semigroup. The perturbed operator is defined using the extension theory for symmetric operators. The resolvent of the perturbed operator is calculated using Krein's formula. It is proven that every rank one perturbation can be approximated in the operator norm. We prove that some form unbounded perturbations can be approximated in the strong resolvent sense without renormalization of the coupling constant only if the original operator is not semibounded. The present approach is applied to study first derivative and Dirac operators with point interaction, in one dimension. 相似文献
17.
We consider the Schr?dinger operator Hγ = ( − Δ)l + γ V(x)· acting in the space
$$L_2 (\mathbb{R}^d ),$$ where 2l ≥ d, V (x) ≥ 0, V (x) is continuous and is not identically zero, and
$$\lim _{|{\mathbf{x}}| \to \infty } V({\mathbf{x}}) = 0.$$ We obtain an asymptotic expansion as
$$\gamma \uparrow 0$$of the bottom negative eigenvalue of Hγ, which is born at the moment γ = 0 from the lower bound λ = 0 of the spectrum σ(H0) of the unperturbed operator H0 = ( − Δ)l (a virtual eigenvalue). To this end we develop a supplement to the Birman-Schwinger theory on the process of the birth of
eigenvalues in the gap of the spectrum of the unperturbed operator H0. Furthermore, we extract a finite-rank portion Φ(λ) from the Birman- Schwinger operator
$$X_V (\lambda ) = V^{\frac{1} {2}} R_\lambda (H_0 )V^{\frac{1}{2}} ,$$ which yields the leading terms for the desired asymptotic
expansion. 相似文献
18.
Some Properties of Essential Spectra of a Positive Operator 总被引:1,自引:1,他引:0
Egor A. Alekhno 《Positivity》2007,11(3):375-386
Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T) of the operator T is a set
, where
is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum
are introduced in the article. The conditions by which
implies either
or
are investigated, where σef(T) is the Fredholm essential spectrum. By this reason, the relations between coefficients of the main part of the Laurent series
of the resolvent R(., T) of a positive operator T around of the point λ = r(T) are studied. The example of a positive integral operator T : L1→ L∞ which doesn’t dominate a non-zero compact operator, is adduced. Applications of results which are obtained, to the spectral
theory of band irreducible operators, are given. Namely, the criteria when the operator inequalities 0 ≤ S < T imply the spectral radius inequality r(S) < r(T), are established, where T is a band irreducible abstract integral operator. 相似文献
19.
After the von Neumann's remark [10] about pathologies of unbounded symmetric operators and an abstract theorem about stability domain [9], we develope here a general theory allowing to construct semibounded restrictions of selfadjoint operators in explicit form. We apply this theory to quantum-mechanical momentum (position) operator to describe corresponding stability domains. Generalization to the case of measurable functions of these operators is considered. In conclusion we discuss spectral properties of self-adjoint extensions of constructed self-adjoint restrictions. 相似文献
20.
V. A. Khatskevich M. I. Ostrovskii V. S. Shulman 《Integral Equations and Operator Theory》2005,51(1):109-119
Inspired by some problems on fractional linear transformations the authors introduce and study the class of operators satisfying the condition
where stands for the spectral radius; and the class of Banach spaces in which all operators satisfy this condition, the authors call such spaces V-spaces. It is shown that many well-known reflexive spaces, in particular, such spaces as Lp(0,1) and Cp, are non-V-spaces if p 2; and that the spaces lp are V-spaces if and only if 1 < p < . The authors pose and discuss some related open problems. 相似文献