Let X be a compact Hausdorff space, let E be a Banach space, and let C(X,E) stand for the Banach space of E-valued continuous functions on X under the uniform norm. In this paper we characterize Integral operators (in the sense of Grothendieck) on C(X,E) spaces in term of their representing vector measures. This is then used to give some applications to Nuclear operators on C(X,E) spaces. AMS(M...

in this paper, we study the chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. in particular, we prove that if t is a remotal subset of an inner product space h, and f is a star-shaped set at a relative chebyshev centre c of t with respect to f, then llx - qt (x)1i2 2 ilx-cll2 + ilc-qt (c) 112 x e f, where qt : f + t is any choice function s...

This paper studies the complex Monge–Ampère equations for F-plurisubharmonic functions in bounded F-hyperconvex domains. We give sufficient conditions this equation to solve measures with a singular part.

Let f (n) 1⁄4 minf (G H ) : G and H are n-chromatic digraphsg and g(n) 1⁄4 minf (G H ) : G andH are n-chromatic graphs}. We prove that f is bounded if and only if g is bounded. 2005 Wiley Periodicals, Inc. J Graph Theory 51:

This paper explores connections between object-oriented programming and Standard ML. In particular we show that F-bounded polymorphism can be expressed using ML's polymorphism and a programming technique we call wrapping. The encoding of F-bounded polymorphism can be used to encode classes as ML modules.

The main aim of this paper is to prove that when 0 < p < 1/2 the maximal operator ∼ σ ∗ p f := sup n∈N |σn f | (n+1)1/p−2 is bounded from the martingale Hardy space Hp to the space Lp, where σn is n -th Fejér mean with respect to bounded Vilenkin system. Mathematics subject classification (2010): 42C10.

We study the connection between uniformly convex functions f : X → R bounded above by ‖ · ‖p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X → R bounded above by ‖ · ‖2 if and only if X admits an equivalent norm with modulus of convexity of power type 2.

If Ωj ∈ Rd are bounded open subsets and Φ ∈ C(Ω1 ; Ω2) respects Lebesgue measure and satisfies F ◦ Φ ∈ BV (Ω1) for all F ∈ BV (Ω2) then Φ is uniformly Lipshitzean. The problem addressed in this note was motivated by the study of the propagation of regularity in the transport by vector fields with bounded divergence,

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

We establish, for $1&lt;p&lt;\\infty$, higher order $\\mathcal{S}^{p}$-differentiability results of the function $\\varphi \\colon t\\in \\mathbb{R} \\mapsto f(A+tK) - f(A)$ selfadjoint operators $A$ and $K$ on a separable Hilbert space $\\mathcal{H}$ with element Schatten class $\\mathcal{S}^{p}(\\mathcal{H})$ $f$ $n$-times differentiable $\\mathbb{R}$. prove that if either $f^{(n)}$ are bound...