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 ...

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...

We establish the complete convergence for arrays of Banach space valued random elements. This result is applied to bootstrapped means of random elements to obtain their strong consistency and is derived in the spirit of Baum-Katz/Hsu-Robbins/Spitzer type convergence. 2000 Mathematics Subject Classification. Primary 60B12; Secondary 60F15.

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

Klaus Schmidt proved that if a strictly stationary sequence of (say) real-valued random variables is such that the family of distributions of its partial sums is tight, then that sequence is a \coboundary". Here Schmidt's result is extended to some (not necessarily stationary) sequences of random variables taking their values in a separable real Banach space.

Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc verifying that sup|z|<1(1−|z|)||f ′(z)|| < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and 1(Y ) if the map ∑∞ n=0 xnz n → (Tn(xn))n defines a bounded linear operator from Bloch(X) into 1(Y )...

Let X1, X2, . . . , Xn be independent random variables and Sk = Pk i=1 Xi. We show that for any constants ak, P( max 1≤k≤n ||Sk| − ak| > 11t) ≤ 30 max 1≤k≤n P(||Sk| − ak| > t). We also discuss similar inequalities for sums of Hilbert and Banach space valued random vectors.

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to the equation d dt (Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our res...

Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ‖Sk‖ with that of ‖Sj‖, and deduce some tail distribution maximal inequalities. The main result of this paper was inspired by the inequality from [dP–M] that says that Pr(‖X1‖ > t) ≤ 5 Pr(‖X1 +X2‖ > t/2) whenever X1 and X2 are independent...

Using the existence of solutions for equilibrium equations with a Neumann type boundary condition as developed by Shi and Liao (J. Inequal. Appl. 2015:363, 2015), we obtain the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space, which are generalizations of in...