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91.
Roman Drnovsek 《Proceedings of the American Mathematical Society》1997,125(4):1081-1087
The concept of quasispectral maximal subspaces for quasinilpotent (but not nilpotent) operators was introduced by M. Omladi\v{c} in 1984. As an application a class of quasinilpotent operators on -spaces, close to the Volterra kernel operator, was studied. In the present Banach function space setting we determine all quasispectral maximal subspaces of analogues of such operators and prove that these subspaces are all the invariant bands. An example is given showing that (in general) they are not all the closed, invariant ideals of the operator.
92.
In this paper we investigate the possibility of using a block‐triangular preconditioner for saddle point problems arising in PDE‐constrained optimization. In particular, we focus on a conjugate gradient‐type method introduced by Bramble and Pasciak that uses self‐adjointness of the preconditioned system in a non‐standard inner product. We show when the Chebyshev semi‐iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble–Pasciak method—the appropriate scaling of the preconditioners—is easily overcome. We present an eigenvalue analysis for the block‐triangular preconditioners that gives convergence bounds in the non‐standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
93.
Piotr Koszmider Przemys?aw Zieliński 《Journal of Mathematical Analysis and Applications》2011,376(1):329-341
Let Γ denote an uncountable set. We consider the questions if a Banach space X of the form C(K) of a given class (1) has a complemented copy of c0(Γ) or (2) for every c0(Γ)⊆X has a complemented c0(E) for an uncountable E⊆Γ or (3) has a decomposition X=A⊕B where both A and B are nonseparable. The results concern a superclass of the class of nonmetrizable Eberlein compacts, namely Ks such that C(K) is Lindelöf in the weak topology and we restrict our attention to Ks scattered of countable height. We show that the answers to all these questions for these C(K)s depend on additional combinatorial axioms which are independent of ZFC ± CH. If we assume the P-ideal dichotomy, for every c0(Γ)⊆C(K) there is a complemented c0(E) for an uncountable E⊆Γ, which yields the positive answer to the remaining questions. If we assume ♣, then we construct a nonseparable weakly Lindelöf C(K) for K of height ω+1 where every operator is of the form cI+S for c∈R and S with separable range and conclude from this that there are no decompositions as above which yields the negative answer to all the above questions. Since, in the case of a scattered compact K, the weak topology on C(K) and the pointwise convergence topology coincide on bounded sets, and so the Lindelöf properties of these two topologies are equivalent, many results concern also the space Cp(K). 相似文献
94.
This paper concerns the use of conjugate residual methods for the solution of nonsymmetric linear systems arising in applications to differential equations. We focus on an application derived from a seismic inverse problem. The linear system is a small perturbation to a symmetric positive-definite system, the nonsymmetries arising from discretization errors in the solution of certain boundary-value problems. We state and prove a new error bound for a class of generalized conjugate residual methods; we show that, in some cases, the perturbed symmetric problem can be solved with an error bound similar to the one for the conjugate residual method applied to the symmetric problem. We also discuss several applications for special distributions of eigenvalues.This work was supported in part by the National Science Foundation, Grants DMS-84-03148 and DCR-81-16779, and by the Office of Naval Research, Contract N00014-85-K-0725. 相似文献
95.
We continue the study of the variety X[M] of planar normal sections on a natural embedding of a flag manifold M. Here we consider those subvarieties of X[M] that are projective spaces. When M=G/T is the manifold of complete flags of a compact simple Lie group G, we obtain our main results. The first one characterizes those subspaces of the tangent space T[T] (M), invariant by the torus action and which give rise to real projective spaces in X[M]. The other one is the following. Let
be the tangent space of the inner symmetric space G/K at [K] . Then RP (
) is maximal in X[M] if and only if 2(G/K) does not vanish. 相似文献
96.
97.
Let
be the quasinilpotent operator without an invariant subspace constructed by C. J. Read. We prove that the modulus of this operator has an invariant subspace (and even an eigenvector). This answers a question posed by Y. Abramovich, C. Aliprantis and O. Burkinshaw. 相似文献
98.
The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh–Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to preconditioning methods, and to other methods for nonsymmetric eigenvalue problems that use the Rayleigh–Ritz procedure. The subject of estimating the boundary of the entire spectrum is briefly discussed, and the importance of preconditioning for interior eigenvalue problems is mentioned. © 1998 John Wiley & Sons, Ltd. 相似文献
99.
Ian N. Deters 《Journal of Mathematical Analysis and Applications》2009,350(1):354-359
In this paper we extend the work done by Deters and Seubert in [I. Deters, S. Seubert, Cyclic vectors of diagonal operators on the space of functions analytic on a disk, J. Math. Anal. Appl. 334 (2007) 1209-1219]. In particular, we shall improve upon a theorem in the aforementioned paper and make connections between the strong operator topology on H(B(0,1)), polynomial behavior on a sequence of points, and the synthesis of diagonal operators on H(B(0,1)). 相似文献
100.
Given a sequence of transition matrices for a nonstationary Markov chain, a matrix whose product on the right of a transition matrix yields the next transition matrix is called a causative matrix. A causative matrix is strongly causative if successive products continue to yield stochastic matrices. This paper presents necessary and sufficient conditions for a matrix to be causative and strongly causative with respect to an invertible transition matrix, by considering the causative matrix as a linear transformation on the rows of the transition matrix. 相似文献