共查询到20条相似文献,搜索用时 46 毫秒
1.
2.
Given a bounded selfadjoint operator a in a Hilbert space , the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for an operator to be in the orbit of a. Also, the orbit of a selfadjoint operator with closed range is provided with a structure of differential manifold.
相似文献
3.
4.
Zoltá n Sebestyé n Jan Stochel 《Proceedings of the American Mathematical Society》2007,135(5):1389-1397
The set of all positive selfadjoint extensions of a positive operator (which is not assumed to be densely defined) is described with the help of the partial order which is relevant to the theory of quadratic forms. This enables us to improve and extend a result of M. G. Krein to the case of not necessarily densely defined operators .
5.
Let 4 be a selfadjoint operator on a Hilbert space H. The results in this paper provide necessary and sufficient conditions on A in order that there exist a nontrivial nonnegative operator D and a unitary operator U with UA = (A − D)U. In one case considered, it is required that the least subspace reducing A, U and containing the range of D is the full Hilbert space. In this case the operators U, D exist if and only if the operator A is not a scalar multiple of the identity and the maximum and minimum of the spectrum of A are not eigenvalues of finite multip icity. This result is used to complete a characterization of the absolute value of a completely nonnormal hyponormal operator. 相似文献
6.
7.
8.
《Journal of Mathematical Analysis and Applications》1986,115(2):470-481
We consider the second-order differential system, (1) (R(t) Y′)′ + Q(t) Y = 0, where R, Q, Y are n × n matrices with R(t), Q(t) symmetric and R(t) positive definite for t ϵ [a, + ∞) (R(t) > 0, t ⩾ a). We establish sufficient conditions in order that all prepared solutions Y(t) of (1) are oscillatory; that is, det Y(t) vanishes infinitely often on [a, + ∞). The conditions involve the smallest and largest eigen-values λn(R−1(t)) and λ1(∝at Q(s) ds), respectively. The results obtained can be regarded as generalizing well-known results of Leighton and others in the scalar case. 相似文献
9.
10.
Mathematische Zeitschrift - 相似文献
11.
Seppo Hassi Adrian Sandovici Henk de Snoo Henrik Winkler 《Acta Mathematica Hungarica》2006,111(1-2):81-105
Summary The sum of two unbounded nonnegative selfadjoint operators is a nonnegative operator which is not necessarily densely defined.
In general its selfadjoint extensions exist in the sense of linear relations (multivalued operators). One of its nonnegative
selfadjoint extensions is constructed via the form sum associated with A and B. Its relations to the Friedrichs and Krein--von Neumann extensions of A+Bare investigated. For this purpose, the one-to-one correspondence between densely defined closed semibounded forms and semibounded
selfadjoint operators is extended to the case of nondensely defined semibounded forms by replacing semibounded selfadjoint
operators by semibounded selfadjoint relations. In particular, the inequality between two closed nonnegative forms is shown
to be equivalent to a similar inequality between the corresponding nonnegative selfadjoint relations.</o:p> 相似文献
12.
13.
Seppo Hassi Michael Kaltenbä ck Henk de Snoo 《Proceedings of the American Mathematical Society》1997,125(9):2681-2692
For a class of closed symmetric operators with defect numbers it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator is semibounded if and only if each one-dimensional restriction of has a generalized Friedrichs extension.
14.
Nezam Iraniparast 《Journal of Mathematical Analysis and Applications》2007,330(1):605-611
We consider a second order hyperbolic system of the type
(1) 相似文献
15.
We define a quotient of bounded operators and on a Hilbert space with a kernel condition as the mapping , . A quotient is said to be positive symmetric if . In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient .
16.
17.
18.
Siberian Mathematical Journal - 相似文献
19.
S. Hassi H. S. V. de Snoo A. D. I. Willemsma 《Proceedings of the American Mathematical Society》1998,126(9):2663-2675
Let be a selfadjoint operator in a Hilbert space with inner product . The rank one perturbations of have the form , , for some element . In this paper we consider smooth perturbations, i.e. we consider for some . Function-theoretic properties of their so-called -functions and operator-theoretic consequences will be studied.