共查询到20条相似文献,搜索用时 15 毫秒
1.
Jussi Laitila 《Integral Equations and Operator Theory》2007,58(4):487-502
Analytic composition operators
are studied on X-valued versions of BMOA, the space of analytic functions on the unit disk that have bounded mean oscillation on the unit
circle, where X is a complex Banach space. It is shown that if X is reflexive and C
φ is compact on BMOA, then C
φ is weakly compact on the X-valued space BMOA
C
(X) defined in terms of Carleson measures. A related function-theoretic characterization is given of the compact composition
operators on BMOA. 相似文献
2.
J.M. Calabuig E.A. Sánchez-Pérez 《Journal of Mathematical Analysis and Applications》2011,373(1):316-321
Let X be a Banach space and E an order continuous Banach function space over a finite measure μ. We prove that an operator T in the Köthe-Bochner space E(X) is a multiplication operator (by a function in L∞(μ)) if and only if the equality T(g〈f,x∗〉x)=g〈T(f),x∗〉x holds for every g∈L∞(μ), f∈E(X), x∈X and x∗∈X∗. 相似文献
3.
The present paper considers the existence of continuous roots of algebraic equations with coefficients being continuous functions defined on compact Hausdorff spaces. For a compact Hausdorff space X, C(X) denotes the Banach algebra of all continuous complex-valued functions on X with the sup norm ∥⋅∥∞. The algebra C(X) is said to be algebraically closed if each monic algebraic equation with C(X) coefficients has a root in C(X). First we study a topological characterization of a first-countable compact (connected) Hausdorff space X such that C(X) is algebraically closed. The result has been obtained by Countryman Jr, Hatori-Miura and Miura-Niijima and we provide a simple proof for metrizable spaces.Also we consider continuous approximate roots of the equation zn−f=0 with respect to z, where f∈C(X), and provide a topological characterization of compact Hausdorff space X with dimX?1 such that the above equation has an approximate root in C(X) for each f∈C(X), in terms of the first ?ech cohomology of X. 相似文献
4.
Let SB(X,Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider π2(X,Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K),H) is in π2(C(K),H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open. 相似文献
5.
Ridgley Lange 《Journal of Mathematical Analysis and Applications》1975,49(3):721-724
The author shows that, for an injective analytic function f, f(T) is almost decomposable iff T is almost decomposable, where T is a bounded linear operator on a Banach space and f(T) is defined by the functional calculus. 相似文献
6.
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
7.
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
8.
Using an isometric version of the Davis, Figiel, Johnson, and Pe?czyński factorization of weakly compact operators, we prove that a Banach spaceX has the approximation property if and only if, for every Banach spaceY, the finite rank operators of norm ≤1 are dense in the unit ball ofW(Y,X), the space of weakly compact operators fromY toX, in the strong operator topology. We also show that, for every finite dimensional subspaceF ofW(Y,X), there are a reflexive spaceZ, a norm one operatorJ:Y→Z, and an isometry Φ :F →W(Y,X) which preserves finite rank and compact operators so thatT=Φ(T) oJ for allT∈F. This enables us to prove thatX has the approximation property if and only if the finite rank operators form an ideal inW(Y,X) for all Banach spacesY. 相似文献
9.
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
10.
Marian Nowak 《Indagationes Mathematicae》2009,20(1):151-403
Let Σ be a σ-algebra of subsets of a non-empty set Ω. Let X be a real Banach space and let X* stand for the Banach dual of X. Let B(Σ, X) be the Banach space of Σ-totally measurable functions f: Ω → X, and let B(Σ, X)* and B(Σ, X)** denote the Banach dual and the Banach bidual of B(Σ, X) respectively. Let bvca(Σ, X*) denote the Banach space of all countably additive vector measures ν: Σ → X* of bounded variation. We prove a form of generalized Vitali-Hahn-Saks theorem saying that relative σ(bvca(Σ, X*), B(Σ, X))-sequential compactness in bvca(Σ, X*) implies uniform countable additivity. We derive that if X reflexive, then every relatively σ(B(Σ, X)*, B(Σ, X))-sequentially compact subset of B(Σ, X)c~ (= the σ-order continuous dual of B(Σ, X)) is relatively σ(B(Σ, X)*, B(Σ, X)**)-sequentially compact. As a consequence, we obtain a Grothendieck type theorem saying that σ(B(Σ, X)*, B(Σ, X))-convergent sequences in B(Σ, X)c~ are σ(B(Σ, X)*, B(Σ, X)**)-convergent. 相似文献
11.
Mohamed Amouch 《Journal of Mathematical Analysis and Applications》2007,326(2):1476-1484
Let T be a bounded linear operator acting on a Banach space X such that T or its adjoint T∗ has the single-valued extension property. We prove that the spectral mapping theorem holds for the B-Weyl spectrum, and we show that generalized Browder's theorem holds for f(T) for every analytic function f defined on an open neighborhood U of σ(T). Moreover, we give necessary and sufficient conditions for such T to satisfy generalized Weyl's theorem. Some applications are also given. 相似文献
12.
Let T ∈ ℒ(X) be a bounded operator on a complex Banach space X. If V is an open subset of the complex plane such that λ-T is of Kato-type for each λ ∈ V, then the induced mapping f(z) ↦ (z-T)f(z) has closed range in the Fréchet space of analytic X-valued functions on V. Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to
a sharper estimate of Nagy’s spectral residuum of T. Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and Putinar and the theory of coherent analytic
sheaves. 相似文献
13.
Vegard Lima 《Journal of Mathematical Analysis and Applications》2007,334(1):593-603
We study the weak metric approximation property introduced by Lima and Oja. We show that a Banach space X has the weak metric approximation property if and only if F(Y,X), the space of finite rank operators, is an ideal in W(Y,X∗∗), the space of weakly compact operators for all Banach spaces Y. 相似文献
14.
Jussi Laitila Pekka J. Nieminen Eero Saksman Hans-Olav Tylli 《Complex Analysis and Operator Theory》2013,7(1):163-181
Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C φ on VMOA implies compactness even from the Bloch space into VMOA. 相似文献
15.
Iryna Banakh Taras Banakh Anatolij Plichko Anatoliy Prykarpatsky 《Central European Journal of Mathematics》2012,10(6):2264-2271
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ? < c the image f(B ?(x)) of each ?-ball B ?(x) ? U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X. 相似文献
16.
In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL
α
1
(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those
which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
Supported by NNSFC No.19671036 相似文献
17.
Tomas P Schonbek 《Journal of Mathematical Analysis and Applications》1977,58(3):527-540
Let be a Banach space; S and T bounded scalar-type operators in . Define Δ on the space of bounded operators on by ΔX = TX ? XS if X is a bounded operator. We set up a calculus for Δ which allows us to consider f(Δ), for f a complex-valued bounded Borel measurable function on the spectrum of Δ, as an operator in the space of bounded operators whose domain is a subspace of operators which we call measure generating. This calculus is used to obtain some results on when the kernel of Δ is a complemented subspace of the space of bounded operators on . 相似文献
18.
V. I. Rybakov 《Mathematical Notes》2007,82(1-2):104-109
The theorem proved in this paper establishes conditions under which a Banach space X is an Asplund space (i.e., its dual space is a space with the Radon-Nikodym (RN) property). The theorem is formulated in terms of the existence of a supersequentially compact set in (B(X **), ω *), where B(X **) stands for the unit ball of the second dual of X and ω* for the weak topology on the ball. The example presented in the paper shows that one cannot get rid of some restrictive conditions in the theorem in general. 相似文献
19.
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
20.
Let X be a complex Banach space and a domain in the complex plane. Let f: → X be an analytic function such that ∥f(ζ)∥ is constant as ζ ? . If X is the complex plane, then by the classical maximum modulus theorem f;(ζ) itself is constant on . This is not the case in general. In the paper we study the norm-constant analytic functions whose values are bounded linear operators over an uniformly convex complex Banach space or, in particular, over a complex Hilbert space. 相似文献