We characterize classes of linear maps between operator spaces E, F which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative L spaces Sp[E ∗] based on the Schatten classes on the separable Hilbert space l. These classes of maps can be viewed as quasi-normed operator ideals in the category of operator spaces, that is in noncommutative (quantized) func...

We consider the completely positive map on the Toeplitz operator system given by conjugation by a composition operator; that is, we analyze operators of the form C∗ φTfCφ We prove that every such operator is weakly asymptotically Toeplitz, and compute its asymptotic symbol in terms of the Aleksandrov-Clark measures for φ. When φ is an inner function, this operator is Toeplitz, and we show under...

Let φ be an odd increasing homeomorphism from R onto R which satisfies φ(0)= 0 and let f : [a,b]×R×R → R be a function satisfying Carathéodory conditions. Separated two-point and periodic boundary value problems containing the nonlinear operator (φ(u′))′, or its more particular form, the so-called p-Laplace operator, have received a lot of attention lately (cf. [6, 7, 8, 14, 15] and the referen...

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...

We introduce an integral-type operator, denoted by P φ , on the space of holomorphic functions on the unit ball B ⊂ C, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of P φ from the weighted Bergman space A p α B to the Bloch-type space Bμ B or the little Bloch-type space Bμ,0 B is calculated. The compactness of the operator is cha...

Every mode of a quantized boson (photon) field is described as a quantum harmonic oscillator. In this description one meets the quantum phase problem, which has been reviewed in the paper [1]. Using the photon annihilation and creation operators â and â†, respectively, which obey the boson commutation relation [â, â†] = 1̂, with 1̂ an identity operator, the number operator is expressed as n̂ = â†â...

Inclusion of absolute summability domains of matrices Factorable matrices Summability method of Cesàro a b s t r a c t In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely conve...

We can write the polynomial solution of the second order linear differential equation of hypergeometric-type φ(x)y + ψ(x)y + λy = 0, where φ and ψ are polynomials, deg φ ≤ 2, degψ = 1 and λ is a constant, among others, by using the Rodrigues operator Rk(φ,u) (see [3]) where u is certain linear operator which satisfies the distributional equation

Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y , respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is defined by σπ(A) = {z ∈ σ(A) : |z| = maxw∈σ(A) |w|}, where σ(A) denotes the spectrum of A. Assume that Φ : A → B is a map and the range of Φ contains all operators with rank at most two. It is pr...