The authors obtain some multiplier theorems on $H^p$ spaces analogous to the classical $L^p$ multiplier theorems of de Leeuw. The main result is that a multiplier operator ${\left(Tf\right)}^{(}x)=\lambda \left(x\right)f̂\left(x\right)$$(\lambda \in C(...$

We generalize some technical results of Glicksberg to the realm of general operator algebras and use them to give a characterization of open and closed projections in terms of certain multiplier algebras. This generalizes a theorem of J. Wells characterizing an important class of ideals in uniform algebras. The difficult implication in our main theorem is that if a projection is open in an operator algebra, then the multiplier algebra of the associated hereditary subalgebra arises as the closure...

We study multipliers M (bounded operators commuting with translations) on weighted spaces L ω p (ℝ), and establish the existence of a symbol µM for M, and some spectral results for translations S t and multipliers. We also study operators T on the weighted space L ω p (ℝ+) commuting either with the right translations S t , t ∈ ℝ+, or left translations P +S −t , t ∈ ℝ+, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ(S t ) of the operator S t proving that...

In 1966 de Branges and Rovnyak introduced a concept of complementation associated to a contraction between Hilbert spaces that generalizes the classical concept of orthogonal complement. When applied to Toeplitz operators on the Hardy space of the disc, H2, this notion turned out to be the starting point of a beautiful subject, with many applications to function theory. The work has been in constant progress for the last few years. We study here the multipliers of some de Branges-Rovnyak spaces...

We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍\mapsto {\Gamma }_{\phi }{⨍}^{\text{'}}\left(S\right)$ to be completely bounded on $H^{\infty }B\left(H\right)$; the Foiaş-Williams-Peller operator | St Γφ | Rφ = | | | 0 S | is then similar to a contraction. We show that if ⨍ : D → B(H) is a bounded analytic function for which $(1-r)\left|\right|{⨍}^{\text{'}}\left(r{e}^{i\theta }\right){\left|\right|}_{B\left(H\right)}^{2}rdrd\theta$ and $(1-r)\left|\right|⨍"\left(r{e}^{i\theta }\right){\left|\right|}_{B\left(H\right)}rdrd\theta$ are Carleson measures, then ⨍ multiplies ${\left(H^1{c}^1\right)}^{\text{'}}$ to itself. Such ⨍ form an algebra A, and when φ’∈ BMO(B(H)), the map $⨍\mapsto {\Gamma }_{\phi }{⨍}^{\text{'}}\left(S\right)$ is bounded $A\to B(H^2\left(H\right),L^2\left(H\right)\ominus H^2\left(H\right))$. Thus we construct a functional calculus for operators of Foiaş-Williams-Peller type.

For subspaces, $X$ and $Y$, of the space, $D$, of all derivatives $M(X,Y)$ denotes the set of all $g\in D$ such that $fg\in Y$ for all $f\in X$. Subspaces of $D$ are defined depending on a parameter $p\in [0,\infty ]$. In Section 6, $M(X,D)$ is determined for each of these subspaces and in Section 7, $M(X,Y)$ is found for $X$ and $Y$ any of these subspaces. In Section 3, $M(X,D)$ is determined for other spaces of functions on $[0,1]$ related to continuity and higher order differentiation.

We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix ${\left(\phi (i+j)\right)}_{i,j\ge 0}$ is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call “shift-bounded”. We show that there is a φ which is a “completely...

Let A be a commutative semisimple Banach algebra, Δ(A) its Gelfand spectrum, T a multiplier on A and T̂ its Gelfand transform. We study the following problems. (a) When is δ(T) = inf{|T̂(f)|: f ∈ Δ(A), T̂(f) ≠ 0} > 0? (b) When is the range T(A) of T closed in A and does it have a bounded approximate identity? (c) How to characterize the idempotent multipliers in terms of subsets of Δ(A)?

Our aim is to study the following new type of multivalued backward stochastic differential equation: $$\left\{\begin{array}{c}-dY\left(t\right)+\partial \phi \left(Y\left(t\right)\right)dt\ni F\left(t,Y\left(t\right),Z\left(t\right),Y_t,Z_t\right)dt+Z\left(t\right)dW\left(t\right),0⩽t⩽T,\\ Y\left(T\right)=\xi ,\end{array}\right.$$ where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.