首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
We characterize the sets X of all products PQ, and Y of all products PQP, where P,Q run over all orthogonal projections and we solve the problems argmin{‖P-Q‖:(P,Q)∈Z}, for Z=X or Y. We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of X.  相似文献   

2.
In this paper, we consider the product of two orthogonal projectionsP andQ on a separable, infinite dimensional Hilbert spaceH. For the operatorQP, there holds the dichotomy:QP is either a Carleman operator or a semi-Fredholm operator with finite defect. Both cases are characterized in terms of the dimensions of the ranges and null spaces ofP andQ and some of their intersections. This extends the case, whereP andQ are the special projections onto the subspaces of time- and band-limited functions inL 2() resp., first considered by Slepian, Pollak and Landau.  相似文献   

3.
Let W and M be two finite dimensional subspaces of a Hilbert space H such that H=WM, and let PWM denote the oblique projection with range W and nullspace M. In this article we get the following formula for the singular values of PWM
  相似文献   

4.
Let T = U|T| and S = V|S| be the polar decompositions. In this paper, we shall obtain the polar decomposition of TS as TS = UWV|TS|, where |T||S*| = W||T||S*|| is the polar decomposition. Next, we shall show that TS = UV|TS| is the polar decomposition if and only if |T| commutes with |S*|. Lastly, we shall apply this result to binormal and centered operators. We shall obtain characterizations of these operator classes from the viewpoint of the polar decomposition.  相似文献   

5.
The main concern of this paper is the perturbation problem for oblique projection generalized inverses of closed linear operators in Banach spaces. We provide a new stability characterization of oblique projection generalized inverses of closed linear operators under T-bounded perturbations, which improves some well known results in the case of the closed linear operators under the bounded perturbation or that the perturbation does not change the null space.  相似文献   

6.
In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore-Penrose inverse. The results are applied to the solution of the equation xbx = x in rings with involution, extending the results of Greville for matrices. Simpler new proofs are given of the Moore-Penrose invertibility of regular elements in rings with involution, and of the Ljance's formula.  相似文献   

7.
8.
The aim of this paper is to give a characterization in Hilbert spaces of the generators of C0-semigroups associated with closed, sectorial forms in terms of the convergence of a generalized Trotter's product formula. In the course of the proof of the main result we also present a similarity result which can be of independent interest: for any unbounded generator A of a C0-semigroup etA it is possible to introduce an equivalent scalar product on the space, such that etA becomes non-quasi-contractive with respect to the new scalar product.  相似文献   

9.
In this study we define some classes of projections in a Hilbert space and extend results obtained in a former paper, [2]. The theory allows better insight into examples described in [2], and it is demonstrated how a certain family of projections can be expressed by means of familiar operators.  相似文献   

10.
A study is made of a recent integral identity of B. Helffer and J. Sjöstrand, which for a not yet fully determined class of probability measures yields a formula for the covariance of two functions (of a stochastic variable); in comparison with the Brascamp-Lieb inequality, this formula is a more flexible and in some contexts stronger means for the analysis of correlation asymptotics in statistical mechanics. Using a fine version of the Closed Range Theorem, the identity's validity is shown to be equivalent to some explicitly given spectral properties of Witten-Laplacians on Euclidean space, and the formula is moreover deduced from the obtained abstract expression for the range projection. As a corollary, a generalised version of Brascamp-Lieb's inequality is obtained. For a certain class of measures occuring in statistical mechanics, explicit criteria for the Witten-Laplacians are found from the Persson-Agmon formula, from compactness of embeddings and from the Weyl calculus, which give results for closed range, strict positivity, essential self-adjointness and domain characterisations.Supported by TMR grant FMRX-CT960001 of the European Commision, PDE and QM at Université de Paris-Sud, France; partly by the Danish Natural Sciences Research Council, grant 9700987.  相似文献   

11.
12.
We consider all convolution tranforms onL 2() which are projections, and determine their ranges and null-spaces; it turns out that all are orthogonal projections. By modification of the kernel, integral transforms are defined which are oblique projections, and their angle of inclination is approximated using finite dimensional spaces. Several families of such projections are treated and results for the angle of inclination as function of the parameters are displayed. In some cases an exact formula has been obtained.  相似文献   

13.
SupposeA is a bounded linear operator on a separable Hilbert space withA m of trace class for some positive integerm. A generalized determinant for the operatorIA is defined, its properties studied and this determinant is then used to exhibit an inversion formula forIA.  相似文献   

14.
Small compact perturbation of strongly irreducible operators   总被引:4,自引:0,他引:4  
An operatorT onH is called strongly irreducible ifT is not similar to any reducible operators. In this paper, we shall say yes to answer the following question raised by D. A. Herrero.Given an operatorT with connected spectrum (T) and a positive number , can we find a compact operatorK with K < such thatT+K is strongly irreducible?Supported by National Natural Science Foundation of China(19901011), Mathematical Center of State Education Commission of China and 973 Project of China  相似文献   

15.
16.
We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition, which turns out to have many applications. From the butterfly decomposition we obtain a one-to-one correspondence between doubly rooted plane trees and free Dyck paths, which implies a simple derivation of a relation between the Catalan numbers and the central binomial coefficients. We also establish a one-to-one correspondence between leaf-colored doubly rooted plane trees and free Schröder paths. The classical Chung-Feller theorem as well as some generalizations and variations follow quickly from the butterfly decomposition. We next obtain two involutions on free Dyck paths and free Schröder paths, leading to parity results and combinatorial identities. We also use the butterfly decomposition to give a combinatorial treatment of Klazar's generating function for the number of chains in plane trees. Finally we study the total size of chains in plane trees with n edges and show that the average size of such chains tends asymptotically to (n+9)/6.  相似文献   

17.
Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C0(N) contraction if and only if , where U is a singular unitary operator with multiplicity and x1, . . . , xd are orthonormal vectors satisfying . For a C0(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors.  相似文献   

18.
In this paper we prove the formula for the expression (A+B)d,W in terms of A,B,W,Ad,W,Bd,W, assuming some conditions for A,B and W. Here Sd,W denotes the generalized W-weighted Drazin inverse of a linear bounded operator S on a Banach space.  相似文献   

19.
Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operatorT is computed in terms of the spectral radius of a generalized inverse ofT. This provides a partial answer to a conjecture of J. Zemánek.  相似文献   

20.
In this paper, we present a comparative study between the variational iteration method and Adomian decomposition method. The study outlines the significant features of the two methods. The analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号