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1.
In this paper we prove the following Krasnosel’skii type fixed point theorem: Let M be a nonempty bounded closed convex subset of a Banach space X. Suppose that A:MX and B:XX are two weakly sequentially continuous mappings satisfying:
(i)
AM is relatively weakly compact;
(ii)
B is a strict contraction;
(iii)
.
Then A+B has at least one fixed point in M.This result is then used to obtain some new fixed point theorems for the sum of a weakly compact and a nonexpansive mapping. The results presented in this paper encompass several earlier ones in the literature.  相似文献   

2.
3.
Let (X,d)(X,d) be a complete metric space and absolute retract for metric spaces. We prove that the common fixed points set of two multivalued operators defined on XX, which have the selection property and satisfy a contraction type condition, is an absolute retract for metric spaces.  相似文献   

4.
We give examples of an Eberlein-compact spaceX such that, ifS x is the unit ball ofC(X)* with thew*-topology then the operatorT: C(X)→C(S x ) defined byTf(μ) = μ(f), f ∈(X), μ ∈ S x , is a non-nice extreme operator.  相似文献   

5.
This paper provides a new fixed point theorem for increasing self-mappings G:BB of a closed ball BX, where X is a Banach semilattice which is reflexive or has a weakly fully regular order cone X+. By means of this fixed point theorem, we are able to establish existence results of elliptic problems with lack of compactness.  相似文献   

6.
Summary Given a compact Hausdorff spaceX, we may associate with every continuous mapa: X X a composition operatorC a onC(X) by the rule(C a f)(x) = f(a(x)). We describe all self-mapsa for whichC a is an algebraic operator or an essentially algebraic operator (i.e. an operator algebraic modulo compact operators), determine the characteristic polynomialp a (z) and the essentially characteristic polynomialq a (z) in these cases and show how the connectivity ofX may be characterized in terms of the quotientsp a (z)/q a (z). Research supported by the Alfried Krupp Förderpreis für junge Hochschullehrer.  相似文献   

7.
Let (Ω, B, μ) be a measure space, X a separable Banach space, and X1 the space of all bounded conjugate linear functionals on X. Let f be a weak1 summable positive B(X, X1)-valued function defined on Ω. The existence of a separable Hilbert space K, a weakly measurable B(X, K)-valued function Q satisfying the relation Q1(ω)Q(ω) = f(ω) is proved. This result is used to define the Hilbert space L2,f of square integrable operator-valued functions with respect to f. It is shown that for B+(X, X1)-valued measures, the concepts of weak1, weak, and strong countable additivity are all the same. Connections with stochastic processes are explained.  相似文献   

8.
Iff:X→Y is a projective morphism between regular varieties over a field, we construct Gysin maps $$f_ * :H^i \left( {X,\Omega _{X/Z}^j } \right) \to H_{f(x)}^{i + d} \left( {X,\Omega _{Y/Z}^j } \right)$$ for the Hodge cohomology groups, whered-dimY-dimX. These Gysin maps have the expected properties, and in particular may be used to construct a cycle class map $$Cl_X :CH^i \left( {X,S} \right) \to H^i \left( {X,\Omega _{X/Z}^i } \right)$$ whereX is quasi-projective over a field,S is the singular locus, andCH i(X, S) is the relative Chow group of codimension-i cycles modulo rational equivalence. Simple properties of this cycle map easily imply the infinite dimensionality theorem for the Chow group of zero cycles of a normal projective varietyX overC with \(H^n \left( {X,\mathcal{O}_X } \right) \ne 0\) , wheren=dimX. One also recovers examples of Nori of affinen-dimensional varieties which support indecomposable vector bundles of rankn.  相似文献   

9.
Let (X,?) be a partially ordered set and d be a complete metric on X. Let F,G be two set-valued mappings on X. We obtained sufficient conditions for the existence of common fixed point of F and G satisfying an implicit relation in partially ordered set X.  相似文献   

10.
We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this pressure.More precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on X.Moreover,the supremum can be attained by a T-invariant measure.  相似文献   

11.
Let be a densely defined operator on a Banach space X. Characterizations of when generates a C0‐semigroup on X are known. The famous result of Lumer and Phillips states that it is so if and only if is dissipative and is dense in X for some . There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kamińska provides perturbation criteria of dissipative operators in terms of ergodic properties. These results, and others, are shown to remain valid in the setting of general non–normable locally convex spaces. Applications of the results to concrete examples of operators on function spaces are also presented.  相似文献   

12.
We prove that there are Tychonoff spaces X for which p(Cp(X)) =? and Cp(X) is a Lindelöf Σ-space while the network weight of X is uncountable. This answers Problem 75 from [4]. An example of a space Y is given such that p(Y)=? and Cp(Y) is a Lindelöf Σ-space, while the network weight of Y is uncountable. This gives a negative answer to Problem 73 from [4]. For a space X with one non-isolated point a necessary and sufficient condition in terms of the topology on X is given for Cp(X) to have countable point-finite cellularity.  相似文献   

13.
14.
We give a purely metric proof of the following result: let (X,d) be a separable metric space; for all ?>0 there is an injectionf ofX inC 0 + such that: $$\forall x,y \in X,d(x, y) \leqq \parallel f(x) - f(y)\parallel _\infty \leqq (3 + \varepsilon )d(x, y).$$ It is a more precise version of a result of I. Aharoni. We extend it to metric space of cardinal α+ (for infinite α).  相似文献   

15.
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,BB(X) satisfy ABN(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:
(a)
There is a bijective bounded linear or conjugate-linear operator S:XX such that ? has the form A?S[f(A)A]S-1.
(b)
The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S−1.
If X has dimension n with 3 ? n < ∞, and B(X) is identified with the algebra Mn of n × n complex matrices, then there exist a map f:MnC?{0}, a field automorphism ξ:CC, and an invertible S ∈ Mn such that ? has one of the following forms:
  相似文献   

16.
Let X be an infinite dimensional real reflexive Banach space with dual space X and GX, open and bounded. Assume that X and X are locally uniformly convex. Let T:XD(T)→2X be maximal monotone and strongly quasibounded, S:XD(S)→X maximal monotone, and C:XD(C)→X strongly quasibounded w.r.t. S and such that it satisfies a generalized (S+)-condition w.r.t. S. Assume that D(S)=LD(T)∩D(C), where L is a dense subspace of X, and 0∈T(0),S(0)=0. A new topological degree theory is introduced for the sum T+S+C, with degree mapping d(T+S+C,G,0). The reason for this development is the creation of a useful tool for the study of a class of time-dependent problems involving three operators. This degree theory is based on a degree theory that was recently developed by Kartsatos and Skrypnik just for the single-valued sum S+C, as above.  相似文献   

17.
18.
Let L(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We characterize additive continuous maps from L(X) onto itself which compress the local spectrum and the convexified local spectrum at a nonzero fixed vector. Additive continuous maps from L(X) onto itself that preserve the local spectral radius at a nonzero fixed vector are also characterized.  相似文献   

19.
《Quaestiones Mathematicae》2013,36(2):141-154
Abstract

Let T be a bounded operator on a Hilbert space H with Von Neumann spectral set X. If there exists no non-zero reducing subspace of H restricted to which T is a normal operator with spectrum contained in the boundary of X and if the uniform algebra R(X) is pointwise boundedly dense in H (X°), then there exists a functional calculus f → f(T) for f ε H (X°). A similar result for the two-variable case is also proved.  相似文献   

20.
Let X be an operator space, let φ be a product on X, and let (X,φ) denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping φ for the algebra (X,φ) to have a completely isometric representation as an algebra of operators on some Hilbert space. In particular, we give an elegant geometrical characterization of such products by using the Haagerup tensor product. Our result makes no assumptions about identities or approximate identities. Our proof is independent of the earlier result of Blecher, Ruan and Sinclair [D.P. Blecher, Z.-J. Ruan, A.M. Sinclair, A characterization of operator algebras, J. Funct. Anal. 89 (1) (1990) 188-201] which solved the case when the bilinear mapping has an identity of norm one, and our result is used to give a simple direct proof of this earlier result. We also develop further the connections between quasi-multipliers of operator spaces and their representations on a Hilbert space or their embeddings in the second dual, and show that the quasi-multipliers of operator spaces defined in [M. Kaneda, V.I. Paulsen, Quasi-multipliers of operator spaces, J. Funct. Anal. 217 (2) (2004) 347-365] coincide with their C-algebraic counterparts.  相似文献   

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