共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced
class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces.
Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result,
we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces.
Received: 10 August 2007 相似文献
2.
Wolfgang Hackenbroch 《Archiv der Mathematik》2009,92(5):485-492
In a Hilbert space context, we propose a rather general notion of “random operators” which allows for taking stochastic limits.
After establishing a connection with measurable fields of closed operators, we may speak of a spectral theory for symmetric
random operators.
Received: 18 December 2008 相似文献
3.
J. R. L. Webb 《Journal of Fixed Point Theory and Applications》2009,5(1):37-45
We show that the concept of a linear operator being u0-positive, and refinements of some classical results of Krasnosel’skiĭ, can be used, in conjunction with the theory of fixed
point index, to give some short proofs of existence and nonexistence of positive solutions for nonlinear maps.
Dedicated to Felix Browder on the occasion of his 80th birthday 相似文献
4.
Isabelle Chalendar Antoine Flattot Nadine Guillotin-Plantard 《Archiv der Mathematik》2008,90(4):353-359
In this paper we study the point spectrum of the operator
where d ≥ 1, 1 ≤ p ≤ ∞([0, 1]
d
) and τ is an irrational rotation on [0, 1]
d
. For a particular class of weights w, the point spectrum of T
w,τ is shown to be empty, generalizing Davie’s result [3], who considered the case p = 2, d = 1.
Received: 1 June 2007, Revised: 16 October 2007 相似文献
5.
Philippa S. Iley 《Journal of Evolution Equations》2007,7(4):765-781
If (A, D(A)) generates a C
0-semigroup T on a Banach space X and then (A + B, D(A)) is also the generator of a C
0-semigroup, S
B
. There are easy examples to show that if T is eventually differentiable then S
B
need not be eventually differentiable. In 1995 an example was constructed to show that if T is immediately differentiable then S
B
need not be immediately differentiable. In this paper we establish necessary and sufficient conditions on the generator (A, D(A)) of T which ensure that eventual or immediate differentiability of T is inherited by S
B
for all . We are therefore able to give a characterization of the immediately and eventually differentiable C
0-semigroups for which differentiability is a stable property under bounded perturbations of the generator. We also prove a
characterization of the C
0-semigroups for which the norm of the resolvent of the generator decays on vertical lines and a new characterization of the
Crandall-Pazy class of semigroups.
We are grateful to Charles Batty and Tom Ransford for helpful discussions and to the referee for their constructive comments. 相似文献
6.
Let X be a nonempty measurable subset of and consider the restriction of the usual Lebesgue measure σ of to X. Under the assumption that the intersection of X with every open ball of has positive measure, we find necessary and sufficient conditions on a L2(X)-positive definite kernel in order that the associated integral operator be nuclear. Taken nuclearity for granted, formulas for the trace of the operator are derived. Some of the results are re-analyzed
when K is just an element of .
相似文献
7.
In this paper we discuss an unusual phenomenon in the context of Toeplitz operators in the Bergman space on the unit disc:
If two Toeplitz operators commute with a quasihomogeneous Toeplitz operator, then they commute with each other. In the Bourbaki
terminology, this result can be stated as follows: The commutant of a quasihomogeneous Toeplitz operator is equal to its bicommutant.
Received: 11 March 2008 相似文献
8.
In this note we prove a generalization of the flat extension theorem of Curto and Fialkow (Memoirs of the American Mathematical
Society, vol. 119. American Mathematical Society, Providence, 1996) for truncated moment matrices. It applies to moment matrices
indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free
setting, this gives an equivalent result for truncated Hankel operators.
相似文献
9.
Christoph Barbian 《Integral Equations and Operator Theory》2008,61(3):299-323
By Beurling’s theorem, the orthogonal projection onto an invariant subspace M of the Hardy space on the unit disk can be represented as where Φ is an inner multiplier of . This concept can be carried over to arbitrary Nevanlinna-Pick spaces but fails in more general settings. This paper introduces
the notion of Beurling decomposable subspaces. An invariant subspace M of a reproducing kernel Hilbert space will be called Beurling decomposable if there exist (operator-valued) multipliers such that and . We characterize the finite-codimensional and the finite-rank Beurling decomposable subspaces by means of their core function
and core operator. As an application, we show that in many analytic Hilbert modules , every finite-codimensional submodule M can be written as with suitable polynomials p
i
.
相似文献
10.
Assume that we have a (compact) Riemann surface S, of genus greater than 2, with , where is the complex unit disc and Γ is a surface Fuchsian group. Let us further consider that S has an automorphism group G in such a way that the orbifold S/G is isomorphic to where is a Fuchsian group such that and has signature σ appearing in the list of non-finitely maximal signatures of Fuchsian groups of Theorems 1 and 2 in [6]. We
establish an algebraic condition for G such that if G satisfies such a condition then the group of automorphisms of S is strictly greater than G, i.e., the surface S is more symmetric that we are supposing. In these cases, we establish analytic information on S from topological and algebraic conditions.
Received: 4 April 2008 相似文献
11.
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
12.
In this paper we develop some unified methods, based on the technique of the auxiliary sublinear operator, for obtaining extensions
of positive linear operators.
In the first part, a version of the Mazur-Orlicz theorem for ordered vector spaces is presented and then this theorem is used
in diverse applications: decomposition theorems for operators and functionals, minimax theory and extensions of positive linear
operators.
In the second part, we give a general sufficient condition (an implication between two inequalities) for the existence of
a monotone sublinear operator and of a positive linear operator. Some particular cases in which this condition becomes necessary
are also studied.
Dedicated to Prof. Romulus Cristescu on his 80th birthday 相似文献
13.
For a given set A⊂Rn a representation theorem for locally defined operators mapping the space Cm(A) of Whitney differentiable functions into C0(A) is presented. 相似文献
14.
Mohamed Bendaoud 《Archiv der Mathematik》2009,92(3):257-265
Let be a complex Hilbert space and let be the algebra of all bounded linear operators on . We characterize additive maps from onto itself preserving different spectral quantities such as the minimum modulus, the surjectivity modulus, and the maximum
modulus of operators.
Received: 15 July 2008 相似文献
15.
We present a norm estimate for the partial transpose map Θ on the tensor product
with respect to a unitarily invariant norm. This is related to the norm estimates of the following maps on Mm,n in terms of the spectral norm of
:
We show further that in the special case of
as well as AX + XB and AX + XBT those estimates are much improved and that
for certain Schatten p-norms.
Dedicated to the memory of late Professor Helmut H. Schaefer 相似文献
16.
S. Shkarin 《Integral Equations and Operator Theory》2009,64(1):115-136
It is shown that if 1 < p < ∞ and X is a subspace or a quotient of an ℓp-direct sum of finite dimensional Banach spaces, then for any compact operator T on X such that ∥I + T∥ > 1, the operator I + T attains its norm. A reflexive Banach space X and a bounded rank one operator T on X are constructed such that ∥I + T∥ > 1 and I + T does not attain its norm.
The author would like to thank E. Shargorodsky for his interest and comments. 相似文献
17.
M. T. Karaev 《Archiv der Mathematik》2009,93(2):147-152
In this paper, we use Banach algebra techniques to prove addition formulas for spectral multiplicities of direct sums of operator
families.
This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) with project 107T649. 相似文献
18.
An operatorX:
is said to be a generalized Toeplitz operator with respect to given contractionsT
1 andT
2 ifX=T
2XT1
*. The purpose of this line of research, started by Douglas, Sz.-Nagy and Foia, and Pták and Vrbová, is to study which properties of classical Toeplitz operators depend on their characteristic relation. Following this spirit, we give appropriate extensions of a number of results about Toeplitz operators. Namely, Wintner's theorem of invertibility of analytic Toeplitz operators, Widom and Devinatz's invertibility criteria for Toeplitz operators with unitary symbols, Hartman and Wintner's theorem about Toeplitz operator having a Fredholm symbol, Hartman and Wintner's estimate of the norm of a compactly perturbed Toeplitz operator, and the non-existence of compact classical Toeplitz operators due to Brown and Halmos.Dedicated to our friend Cora Sadosky on the occasion of her sixtieth birthday 相似文献
19.
We study functions f(z) holomorphic in having the property f(z) ≠ 0 for 0 < Im z < 1 and we obtain lower bounds for |f(z)| for 0 < Im z < 1. In our analysis we deal with scalar functions f(z) as well as with operator valued holomorphic functions I + A(z) assuming that A(z) is a trace class operator for and I + A(z) is invertible for 0 < Im z < 1 and is unitary for .
A. Borichev was partially supported by the ANR project DYNOP. 相似文献
20.
Sebastian Król 《Journal of Evolution Equations》2009,9(3):449-468
The concept of the gap function is used to give new perturbation results for generators of holomorphic semigroups. In particular, we show that if A is the generator of a holomorphic semigroup on a Banach space and , then every closed linear operator C such that for some and
generates a holomorphic semigroup, too. Moreover, we obtain an analogue of this result for differences of semigroups. If T is a holomorphic semigroup and , then every C
0-semigroup S with
is holomorphic. We also give certain estimates for the constants M
A
and k
T
appearing in the above conditions.
The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW
grant Nr N201384834. 相似文献