Nuclear Operators on Spaces of Continuous Vector-Valued Functions
نویسنده
چکیده
Abstract Let Ω be a compact Hausdorff space, let E be a Banach space, and let C(Ω, E) stand for the Banach space of all E-valued continuous functions on Ω under supnorm. In this paper we study when nuclear operators on C(Ω, E) spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if F is a Banach space and if T : C(Ω, E) → F is a nuclear operator, then T induces a bounded linear operator T from the space C(Ω) of scalar valued continuous functions on Ω into N (E, F ) the space of nuclear operators from E to F , in this case we show that E has the Radon-Nikodym property if and only if T is nuclear whenever T is nuclear.
منابع مشابه
POINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS
The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let be a non-emp...
متن کاملCompact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کاملBilateral composition operators on vector-valued Hardy spaces
Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{ph, T}: f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq +infty$. Compactness and weak compactness of $C_{ph, T}$ on $H^p(X)$ are characterized an...
متن کاملRemarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''
In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...
متن کاملOperator Valued Series and Vector Valued Multiplier Spaces
Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous linear operators from $X$ into $Y$. If ${T_{j}}$ is a sequence in $L(X,Y)$, the (bounded) multiplier space for the series $sum T_{j}$ is defined to be [ M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}% T_{j}x_{j}text{ }converges} ] and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...
متن کامل