共查询到20条相似文献,搜索用时 12 毫秒
1.
Danrun Huang 《Integral Equations and Operator Theory》1992,15(3):454-469
LetA be a matrix over a complex commutative unital Banach algebra. We give necessary and sufficient conditions forA to have a generalized inverse. Moreover, if the Banach algebra has a symmetric involution, these are also necessary and sufficient conditions forA to admit the Moore-Penrose inverse.Partially supported by NSF Grant DMS-8802593 相似文献
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The convergence of the class of direct interpolatory iterationsI
n
for a simple zero of a non-linear operatorF in a Banach space of finite or infinite dimension is studied.A general convergence result is established and used to show that ifF is entire the radius of convergence goes to infinity withn while ifF is analytic in a ball of radiusR the radius of convergence increases to at leastR/2 withn.The research was supported in part by the National Science Foundation under Grant MCS 75-222-55 and the office of Naval Research under Contract N00014-76-C-0370, NR 044-422. 相似文献
4.
We consider upper-triangular 2-by-2 operator matrices and are interested in the set that has to be added to certain spectra of the matrix in order to get the union of the corresponding spectra of the two diagonal operators. We show that in the cases of the Browder essential approximate point spectrum, the upper semi-Fredholm spectrum, or the lower semi-Fredholm spectrum the set in question need not to be an open set but may be just a singleton. In addition, we modify and extend known results on Hilbert space operators to operators on Banach spaces. 相似文献
5.
Ronalda Benjamin 《Quaestiones Mathematicae》2016,39(5):643-664
This paper illustrates some initial steps taken in the e?ort of unifying the theory of positivity in ordered Banach algebas (OBAs) with the general Fredholm theory in Banach algebras. We introduce here upper Weyl and upper Browder elements in an OBA relative to an arbitrary Banach algebra homomorphism and investigate the spectra corresponding to the sets of upper Weyl and upper Browder elements, which we shall refer to as the upper Weyl and upper Browder spectra, respectively. 相似文献
6.
Let L(H) be the algebra of all bounded linear operators on an infinite dimensional complex Hilbert H. We characterize linear maps from L(H) onto itself that preserve the essential spectral radius. 相似文献
7.
The solvability of integral equations of the form
and the behaviour of the solution x at infinity are investigated. Conditions on k and on a weight function w are obtained which ensure that the integral operator K with kernel k is bounded as an operator on Xw, where Xw denotes the weighted space of those continuous functions defined on the half-line which are O(w(s)) as
We also derive conditions on w and k which imply that the spectrum and essential spectrum of K on Xw are the same as on BC[0,). In particular, the results apply when
when the integral equation is of Wiener-Hopf type. In this case we show that our results are particularly sharp. 相似文献
8.
Sahbi Boussandel 《Journal of Differential Equations》2011,250(2):929-948
In this article, we use a Galerkin method to prove a maximal regularity result for the following abstract gradient system
9.
J. J. Koliha 《Aequationes Mathematicae》1977,16(1-2):31-35
The paper gives a necessary and sufficient condition on the spectrum of a bounded linear operator on Banach space for the convergence of the series
0
T(I-T
2)
n
. Some properties of the sum are investigated. 相似文献
10.
The 2×2 system of integral equations corresponding to the biharmonic single layer potential in 2 is known to be strongly elliptic. It is also known to be positive definite on a space of functions orthogonal to polynomials of degree one. We study the question of its unique solvability without this orthogonality condition. To each curve , we associate a 4×4 matrixB
such that this problem for the family of all curves obtained from by scale transformations is equivalent to the eigenvalue problem forB
. We present numerical approximations for this eigenvalue problem for several classes of curves. 相似文献
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We characterize the existence and uniqueness of solutions of an abstract fractional differential equation with infinite delay in Hölder spaces. 相似文献
13.
Manuel González 《Journal of Functional Analysis》2003,200(1):65-70
We give a negative answer to the perturbation classes problem: the perturbation class of the upper semi-Fredholm operators contains properly the strictly singular operators, and the perturbation class of the lower semi-Fredholm operators contains properly the strictly cosingular operators. 相似文献
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When A∈B(H) and B∈B(K) are given, we denote by MC the operator matrix acting on the infinite-dimensional separable Hilbert space H⊕K of the form In this paper, for given A and B, the sets and ?C∈Inv(K,H)σl(MC) are determined, where σl(T),Bl(K,H) and Inv(K,H) denote, respectively, the left spectrum of an operator T, the set of all the left invertible operators and the set of all the invertible operators from K into H. 相似文献
16.
Danrun Huang 《Integral Equations and Operator Theory》1993,17(1):54-67
For a matrix over a complex commutative unital Banach algebra, necessary and sufficient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earlier work of the author. 相似文献
17.
Câlin-Grigore Ambrozie 《Integral Equations and Operator Theory》1996,25(1):1-34
We prove the stability of the index of a Fredholm complex of Banach spaces under those compact perturbations which are uniform limits of finite-rank operators (Theorem 3.3). This result is a consequence of some similar statements (Theorems 3.1 and 3.2) concerning more general objects, namely the Fredholm pairs (Definition 1.1). 相似文献
18.
Using a generalized notion of symplectic Cayley transform in the symplectic group, we introduce a sequence of integer valued invariants (higher order signatures) associated with a degeneracy instant of a smooth path of symplectomorphisms. In the real analytic case, we give a formula for the Conley–Zehnder index in terms of the higher order signatures. 相似文献
19.
We give a matrix representation for the resolvent of the Friedrichs extension of some semibounded 2×2 operator matrices and study their essential spectrum. 相似文献
20.
《Quaestiones Mathematicae》2013,36(6):811-822
AbstractIn this note we investigate regularities (semiregularities) R and S in a Banach algebra A satisfying S ? R and the corresponding spectra σS and σR Satisfying
sup {|λ| : λ ∈ σR(a)} = sup{|λ| : λ ∈ σS (a)} 相似文献