We give definitions and some properties of the shift operator SL(H2) and multiplication operator on L(H ). In addition, we obtain some properties of the commutant of the shift operator SL(H2) and characterize SL(H2)-invariant subspaces.

The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of C∞-vectors of a self-adjoint operator, is considered in the framework of the so-called duality method. The multiplication is defined by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain...

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the unif...

acting in L(R). This means that we consider a system of N interacting quantum particles in R. Here x = (x1, . . . , xN ) ∈ R Nd is for the joint position vector, where each component xj ∈ R d represents the position of the jth particle, 1 ≤ j ≤ N . Next, ∆ stands for the Laplacian in R. The interaction energy operator U(x) acts as multiplication by a function U(x). Finally, the term V(ω;x) repr...

Let φ and ψ be holomorphic maps on such that φ( ) ⊂ . Let Cφ,Mψ and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces AβN to Bloch-type spaces. In fact, we prove that these operators map AβN compactly into Bloch-type spaces if and only if they map A β...

Let T be a bounded operator on a complex Banach space X. If V is an open subset of the complex plane, we give a condition sufficient for the mapping f(z) 7→ (T − z)f(z) to have closed range in the Fréchet space H(V, X) of analytic X-valued functions on V . Moreover, we show that there is a largest open set U for which the map f(z) 7→ (T − z)f(z) has closed range in H(V, X) for all V ⊆ U . Final...