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51.
Mark Pankov 《Archiv der Mathematik》2008,90(6):528-529
Let H be a separable complex Hilbert space and be the Grassmannian of closed subspaces with infinite dimension and codimension. We show that every order preserving bijective
transformation of is induced by an invertible bounded semi-linear operator.
Received: 23 October 2007 相似文献
52.
Marcus Carlsson 《Integral Equations and Operator Theory》2008,61(4):593-598
In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M
z
on a Hilbert space -valued analytic functions, where M
z
denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s
theorem.
In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works
for Banach space operators.
相似文献
53.
Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?
We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:
相似文献
- when V(G) is the union of two cliques
- when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.
54.
Let H be a subgroup of a finite group G, and assume that p is a prime that does not divide |G : H|. In favorable circumstances, one can use transfer theory to deduce that the largest abelian p-groups that occur as factor groups of G and of H are isomorphic. When this happens, Tate’s theorem guarantees that the largest not-necessarily-abelian p-groups that occur as factor groups of G and H are isomorphic. Known proofs of Tate’s theorem involve cohomology or character theory, but in this paper, a new elementary
proof is given. It is also shown that the largest abelian p-factor group of G is always isomorphic to a direct factor of the largest abelian p-factor group of H.
Received: 17 June 2008 相似文献
55.
The De Donder–Weyl (DW) Hamilton–Jacobi equation is investigated in this paper, and the connection between the DW Hamilton–Jacobi
equation and multi-symplectic Hamiltonian system is established. Based on the DW Hamilton–Jacobi theory, generating functions
for multi-symplectic Runge–Kutta (RK) methods and partitioned Runge–Kutta (PRK) methods are presented.
The work is supported by the Foundation of ICMSEC, LSEC, AMSS and CAS, the NNSFC (No.10501050, 19971089 and 10371128) and
the Special Funds for Major State Basic Research Projects of China (2005CB321701). 相似文献
56.
Bertalan Pécsi 《Algebra Universalis》2009,60(4):369-380
We prove that the class of weakly representable relation algebras is closed under homomorphic images, hence it is a variety.
As a corollary we classify the subdirectly irreducible algebras in this class.
Received April 3, 2007; accepted in final form February 7, 2008. 相似文献
57.
Multiplication operators in weighted Banach (and locally convex) spaces of functions holomorphic in the unit disc are well
known. In this note we investigate the connection between power boundedness, mean ergodicity and uniform mean ergodicity of
such operators.
Received: 13 October 2008, Revised: 18 November 2008 相似文献
58.
We prove that several types of open Riemann surfaces, including the finitely connected planar domains, embed properly into
such that the values on any given discrete sequence can be arbitrarily prescribed.
Kutzschebauch supported by Schweizerische Nationalfonds grant 200021-107477/1. 相似文献
59.
We develop a theoretical framework for projection-iterative methods to solve operator equations of the form Au + Bu = f, where A is a Toeplitz operator in a Banach space , B is considered as a perturbation (of general form) of A, and f is a given element in this space. The methods are adopted for application to general situations, in particular, to the equations
in which A need not be a Fredholm operator. The idea to involve iteration procedures and the technique which we apply allow to obtain
conditions on perturbations for convergence and effective error estimates in terms of some weighted spaces (without any restrictions
on the norms for perturbations). Based on established evaluations we derive further information about decaying properties
of the solutions. The obtained results are illustrated by considering concrete classes of equations as, for instance, equations
corresponding to Jacobi type operators.
相似文献
60.
Let A be a unital C*-algebra with non-zero socle (soc(A)). We introduce the essential conorm of an element a in A (denoted by γ
e
(a)), as the conorm of the element π(a), where π denotes the canonical projection of A onto . It is established that for every von Neumann regular element , γ
e
(a) = max . We characterize the continuity points of the conorm and essential conorm for extremally rich C*-algebras. Some formulae for the distance from zero to the generalized spectrum and Atkinson spectrum are also obtained.
Authors partially supported by I+D MEC projects no. MTM2005-02541 and MTM2007-65959, and Junta de Andalucía grants FQM0199
and FQM1215. 相似文献