共查询到20条相似文献,搜索用时 53 毫秒
1.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2008,340(1):366-373
A Banach space operator T∈B(X) is hereditarily polaroid, T∈HP, if every part of T is polaroid. HP operators have SVEP. It is proved that if T∈B(X) has SVEP and R∈B(X) is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T∗+Q∗ satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If A∈B(X) is an algebraic operator which commutes with the polynomially HP operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of σ(T+N), and f∗(T+N) satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of σ(T+N). 相似文献
2.
Jian YuDingtao Peng Shuwen Xiang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6326-6332
Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. 相似文献
3.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2005,308(2):578-587
A Banach space operator T∈B(X) is said to be totally hereditarily normaloid, T∈THN, if every part of T is normaloid and every invertible part of T has a normaloid inverse. The operator T is said to be an H(q) operator for some integer q?1, T∈H(q), if the quasi-nilpotent part H0(T−λ)=(T−λ)−q(0) for every complex number λ. It is proved that if T is algebraically H(q), or T is algebraically THN and X is separable, then f(T) satisfies Weyl's theorem for every function f analytic in an open neighborhood of σ(T), and T∗ satisfies a-Weyl's theorem. If also T∗ has the single valued extension property, then f(T) satisfies a-Weyl's theorem for every analytic function f which is non-constant on the connected components of the open neighborhood of σ(T) on which it is defined. 相似文献
4.
Surjit Singh Khurana 《Journal of Mathematical Analysis and Applications》2009,350(1):290-293
Let X be a completely regular Hausdorff space, E Hausdorff a quasi-complete locally convex space and Cb(X,E) all E-valued bounded continuous functions on X with strict topologies βt, , . We prove that a linear continuous mapping T:Cb(X,E)→E arises from a scalar measure μ∈(Cb′(X),βz)(z=t,∞,τ) if and only if g(T(f))=0 whenever g○f=0 for any f∈Cb(X,E), g∈E′. 相似文献
5.
《复变函数与椭圆型方程》2012,57(10):827-835
The analytic map g on the unit disk D is said to induce a multiplication operator L from the Banach space X to the Banach space Y if L(f)=f·g∈Y for all f∈X. For z ∈ D and α>0 the families of weighted Cauchy transforms Fα are defined by ?(z) = ∫T Kx α (z)dμ(x) where μ(x) is complex Borel measures, x belongs to the unit circle T and the kernel Kx (z) = (1- xz)?1. In this article we will explore the relationship between the compactness of the multiplication operator L acting on F 1 and the complex Borel measures μ(x). We also give an estimate for the essential norm of L 相似文献
6.
Pei-Kee Lin 《Journal of Mathematical Analysis and Applications》2005,312(1):138-147
Let (X,F,μ) be a complete probability space, B a sub-σ-algebra, and Φ the probabilistic conditional expectation operator determined by B. Let K be the Banach lattice {f∈L1(X,F,μ):‖Φ(|f|)‖∞<∞} with the norm ‖f‖=‖Φ(|f|)‖∞. We prove the following theorems:
- (1)
- The closed unit ball of K contains an extreme point if and only if there is a localizing set E for B such that supp(Φ(χE))=X.
- (2)
- Suppose that there is n∈N such that f?nΦ(f) for all positive f in L∞(X,F,μ). Then K has the uniformly λ-property and every element f in the complex K with is a convex combination of at most 2n extreme points in the closed unit ball of K.
7.
O. Blasco J.M. Calabuig T. Signes 《Journal of Mathematical Analysis and Applications》2008,348(1):150-164
Given three Banach spaces X, Y and Z and a bounded bilinear map , a sequence x=n(xn)⊆X is called B-absolutely summable if is finite for any y∈Y. Connections of this space with are presented. A sequence x=n(xn)⊆X is called B-unconditionally summable if is finite for any y∈Y and z∗∈Z∗ and for any M⊆N there exists xM∈X for which ∑n∈M〈B(xn,y),z∗〉=〈B(xM,y),z∗〉 for all y∈Y and z∗∈Z∗. A bilinear version of Orlicz-Pettis theorem is given in this setting and some applications are presented. 相似文献
8.
We study the Pettis integral for multi-functions defined on a complete probability space (Ω,Σ,μ) with values into the family cwk(X) of all convex weakly compact non-empty subsets of a separable Banach space X. From the notion of Pettis integrability for such an F studied in the literature one readily infers that if we embed cwk(X) into ?∞(BX∗) by means of the mapping defined by j(C)(x∗)=sup(x∗(C)), then j○F is integrable with respect to a norming subset of B?∞∗(BX∗). A natural question arises: When is j○F Pettis integrable? In this paper we answer this question by proving that the Pettis integrability of any cwk(X)-valued function F is equivalent to the Pettis integrability of j○F if and only if X has the Schur property that is shown to be equivalent to the fact that cwk(X) is separable when endowed with the Hausdorff distance. We complete the paper with some sufficient conditions (involving stability in Talagrand's sense) that ensure the Pettis integrability of j○F for a given Pettis integrable cwk(X)-valued function F. 相似文献
9.
Caishi Wang 《Journal of Mathematical Analysis and Applications》2007,329(2):913-921
Let δa be the Dirac delta function at a∈R and (E)⊂(L2)⊂∗(E) the canonical framework of white noise analysis over white noise space (E∗,μ), where E∗=S∗(R). For h∈H=L2(R) with h≠0, denote by Mh the operator of multiplication by Wh=〈⋅,h〉 in (L2). In this paper, we first show that Mh is δa-composable. Thus the delta function δa(Mh) makes sense as a generalized operator, i.e. a continuous linear operator from (E) to ∗(E). We then establish a formula showing an intimate connection between δa(Mh) as a generalized operator and δa(Wh) as a generalized functional. We also obtain the representation of δa(Mh) as a series of integral kernel operators. Finally we prove that δa(Mh) depends continuously on a∈R. 相似文献
10.
B.P. Duggal 《Linear algebra and its applications》2006,414(1):271-277
A Banach space operator T is polaroid and satisfies Weyl’s theorem if and only if T is Kato type at points λ ∈ iso σ(T) and has SVEP at points λ not in the Weyl spectrum of T. For such operators T, f(T) satisfies Weyl’s theorem for every non-constant function f analytic on a neighborhood of σ(T) if and only if f(T∗) satisfies Weyl’s theorem. 相似文献
11.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2009,359(2):631-636
A Banach space operator T∈B(X) satisfies Browder's theorem if the complement of the Weyl spectrum σw(T) of T in σ(T) equals the set of Riesz points of T; T is polaroid if the isolated points of σ(T) are poles (no restriction on rank) of the resolvent of T. Let Φ(T) denote the set of Fredholm points of T. Browder's theorem transfers from A,B∈B(X) to S=LARB (resp., S=A⊗B) if and only if A and B∗ (resp., A and B) have SVEP at points μ∈Φ(A) and ν∈Φ(B) for which λ=μν∉σw(S). If A and B are finitely polaroid, then the polaroid property transfers from A∈B(X) and B∈B(Y) to LARB; again, restricting ourselves to the completion of X⊗Y in the projective topology, if A and B are finitely polaroid, then the polaroid property transfers from A∈B(X) and B∈B(Y) to A⊗B. 相似文献
12.
William Dimbour 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2351-2357
Using spectral theory we obtain sufficient conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form x′(t)=A(t)x([t])+f(t),t∈R, where A(t) is an almost automorphy operator, f(t) is an X-valued almost automorphic function and X is a finite dimensional Banach space. 相似文献
13.
Dhruba R. Adhikari 《Journal of Mathematical Analysis and Applications》2008,348(1):122-136
Let X be a real reflexive Banach space with dual X∗. Let L:X⊃D(L)→X∗ be densely defined, linear and maximal monotone. Let T:X⊃D(T)→X∗2, with 0∈D(T) and 0∈T(0), be strongly quasibounded and maximal monotone, and C:X⊃D(C)→X∗ bounded, demicontinuous and of type (S+) w.r.t. D(L). A new topological degree theory has been developed for the sum L+T+C. This degree theory is an extension of the Berkovits-Mustonen theory (for T=0) and an improvement of the work of Addou and Mermri (for T:X→X∗2 bounded). Unbounded maximal monotone operators with are strongly quasibounded and may be used with the new degree theory. 相似文献
14.
Alexandru Mihail Radu Miculescu 《Journal of Mathematical Analysis and Applications》2011,376(1):187-192
For an infinite-dimensional Banach space X, S and T bounded linear operators from X to X such that ‖S‖,‖T‖<1 and w∈X, let us consider the IFS Sw=(X,f1,f2), where f1,f2:X→X are given by f1(x)=S(x) and f2(x)=T(x)+w, for all x∈X. We prove that if the operator S is finite-dimensional, then the set {w∈X|the attractor of Sw is not connected} is open and dense in X. 相似文献
15.
E. Jiménez Fernández 《Journal of Mathematical Analysis and Applications》2011,383(1):130-136
Consider a Banach function space X(μ) of (classes of) locally integrable functions over a σ-finite measure space (Ω,Σ,μ) with the weak σ-Fatou property. Day and Lennard (2010) [9] proved that the theorem of Komlós on convergence of Cesàro sums in L1[0,1] holds also in these spaces; i.e. for every bounded sequence n(fn) in X(μ), there exists a subsequence k(fnk) and a function f∈X(μ) such that for any further subsequence j(hj) of k(fnk), the series converges μ-a.e. to f. In this paper we generalize this result to a more general class of Banach spaces of classes of measurable functions — spaces L1(ν) of integrable functions with respect to a vector measure ν on a δ-ring — and explore to which point the Fatou property and the Komlós property are equivalent. In particular we prove that this always holds for ideals of spaces L1(ν) with the weak σ-Fatou property, and provide an example of a Banach lattice of measurable functions that is Fatou but do not satisfy the Komlós Theorem. 相似文献
16.
Wojciech Jab?oński 《Journal of Mathematical Analysis and Applications》2005,312(2):527-534
Assume that and are uniformly continuous functions, where D1,D2⊂X are nonempty open and arc-connected subsets of a real normed space X. We prove that then either f and g are affine functions, that is f(x)=x∗(x)+a and g(x)=x∗(x)+b with some x∗∈X∗ and a,b∈R or the algebraic sum of graphs of functions f and g has a nonempty interior in a product space X×R treated as a normed space with a norm . 相似文献
17.
Raúl E. Curto Young Min Han 《Journal of Mathematical Analysis and Applications》2007,336(2):1424-1442
We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of σ(T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f∈H((T)), the space of functions analytic on an open neighborhood of σ(T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f∈H(σ(T)). 相似文献
18.
D. Azagra 《Journal of Functional Analysis》2007,242(1):1-36
We characterize the class of separable Banach spaces X such that for every continuous function and for every continuous function there exists a C1 smooth function for which |f(x)−g(x)|?ε(x) and g′(x)≠0 for all x∈X (that is, g has no critical points), as those infinite-dimensional Banach spaces X with separable dual X∗. We also state sufficient conditions on a separable Banach space so that the function g can be taken to be of class Cp, for p=1,2,…,+∞. In particular, we obtain the optimal order of smoothness of the approximating functions with no critical points on the classical spaces ?p(N) and Lp(Rn). Some important consequences of the above results are (1) the existence of a non-linear Hahn-Banach theorem and the smooth approximation of closed sets, on the classes of spaces considered above; and (2) versions of all these results for a wide class of infinite-dimensional Banach manifolds. 相似文献
19.
20.
Shuhuang Xiang 《Journal of Mathematical Analysis and Applications》2004,290(1):310-315
Let X be a uniformly smooth infinite dimensional Banach space, and (Ω,Σ,μ) be a σ-finite measure space. Suppose that T:X→L∞(Ω,Σ,μ) satisfies
(1−ε)‖x‖?‖Tx‖?‖x‖,∀x∈X, 相似文献