A. In this article we prove that the n linear operator whose symbol is the characteristic function of the simplex ∆n = ξ1 < ... < ξn is bounded from L2 × ... × L2 into L2/n, generalizing in this way our previous work on the “bi-est” operator [12], [13] (which corresponds to the case n = 3) as well as the Lacey Thiele theorem on the bi-linear Hilbert transform [7], [8] (which corresponds ...

Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T 〈Tx, y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be esta...

We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a C0−semigroup and one linear bounded operator with Wick-type multiplication, all of them set in the infinite dimensional space framework of white noise analysis. We prove existence and uniqueness of solutions for this class of SPDEs. In particular, we al...

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s sub...

A consequence of Littlewood’s Subordination Principle [10] is the (not at all obvious) fact that every composition operator restricts to a bounded operator on the Hardy space H2 (see also [5, Theorem 1.7, page 10] or [16, pp. 13–15]), and this in turn has inspired a lively enterprise connecting complex function theory with operator theory, the goal being to understand how properties Cφ are rela...

Given separable Banach spaces X, Y , Z and a bounded linear operator T : X → Y , then T is said to preserve a copy of Z provided that there exists a closed linear subspace E of X isomorphic to Z and such that the restriction of T to E is an into isomorphism. It is proved that every operator on C([0, 1]) which preserves a copy of an asymptotic ℓ1 space also preserves a copy of C([0, 1]).

We study linear evolution equations in separable Hilbert spaces defined by a bounded operator. answer the question which of these can be written as gradient flow, namely those for operator is real diagonalisable. The proof constructive, from we also derive geodesic lambda-convexity.