In this paper some new positive results in the Operator Corona Problem are obtained in rather general situation. The main result is that under some additional assumptions about a bounded analytic operator-valued function F in the unit disc D the condition F (z)F (z) ≥ δI ∀z ∈ D (δ > 0) implies that F has a bounded analytic left inverse. Typical additional assumptions are (any of the following):...

This paper deals with the so-called A-numerical radius associated a positive (semi-definite) bounded linear operator A acting on complex Hilbert space H. Several new inequalities involving this concept are established. In particular, we prove several estimates for 2×2 matrices whose entries A-bounded operators. Some of obtained results cover and extend well-known recent due to Bani-Domi Kittane...

We study Cesàro (C, δ) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x1, x2) ∈ R2 : 0 ≤ x1 ≤ x2 ≤ 1}. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C, δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ > ...

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

In a number of papers ([1], [2]), Delves and Mead have derived some useful (though limited) rate of convergence results which can be applied to variational approximations for the solution of linear positive definite operator equations when the coordinate system is uniformly asymptotically diagonal. Independently, Mikhlin [5] has examined the stability of such variational approximations in the c...

Improving upon a recent result of L. Coburn and J. Xia, we show that for any bounded linear operator T on the Segal-Bargmann space, the Berezin transform of T is a function whose partial derivatives of all orders are bounded. Similarly, if T is a bounded operator on any one of the usual weighted Bergman spaces on a bounded symmetric domain, then the appropriately defined “invariant derivatives”...

amalgam space W (C,L2(R, T 1 1 )) which is locally continuous and globally L2. We show that the sampling or discretization operator R from S to l2(Z, T 1 1 ) is a bounded linear operator. We introduce the dilated spaces S∆ = D∆ S parametrized by the coarseness ∆, and show that the discretization operator is also bounded with a bounded inverse for any ∆ ∈ Zn. This allows us to represent discrete...

In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

Our object is to give an overview of some basic results about holomorphic mappings of circular domains in various spaces of operators. We begin by considering C*-algebras and pass to J*-algebras and other spaces when this seems natural. Our first result is a simple extension of the maximum principle where the unitary operators play the role of the unit circle. We illustrate the power of this re...

In the presented research, uniqueness and existence of a mild solution for fractional system semilinear evolution equations with infinite delay an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative non-integer-order 1<??2 parameter 0<?<1 used to establish our model. ?-Laplace transform strongly continuous cosine sine families uniformly bounde...