We prove that if n closed disks D1, D2,. . . , Dn, of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then their intersection D1 ∩ D2 · · · ∩ Dn is a complete K-spectral set for A, with K ≤ n + n(n−1)/ √ 3. When n = 2 and the intersection X1∩X2 is an annulus, this result gives a positive answer to a question of A.L. Shields (1974).

and Applied Analysis 3 Krein-Rutman theorem see 34 , we infer that if r B / 0, then there exist φ ∈ P \ {θ} and g∗ ∈ P ∗ \ {θ} such that Bφ r B φ, B∗g∗ r B g∗. 2.1 For a given constant δ > 0, set P ( g∗, δ ) { x ∈ P, g∗ x ≥ δ‖x‖, 2.2 then P g∗, δ is also a cone in E. Definition 2.1 see 30 . Let D ⊂ E and F : D → E a nonlinear operator. F is said to be quasiadditive on lattice, if there exists y...

In this paper, we consider a linear operator of the Korteweg-de Vries type Lu = ?u ?y + R2(y)?3u ?x3 R1(y)?u ?x R0(y)u initially defined on C? 0,?(??), where ?? {(x, y) : ? x ?,?? < y ?}. 0,?(??) is set infinitely differentiable compactly supported function with respect to variable and satisfying conditions: u(i) (??, (?, y), i 0, 1, 2. With coefficients L , assume that these are continuous ...

The aim of this paper is to solve the tracking problem for linear periodic discrete-time systems with independent random perturbations, in Hilbert spaces. Under stabilizability conditions, we will find an optimal control, which minimize the cost function associated to this problem, in the case when the control weight cost is only nonnegative and not necessarily uniformly positive. 2000 Mathemat...

In the present paper, we study some approximation properties of the Szász type operators involving Charlier polynomials introduced by Varma and Taşdelen in 2012. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain the error in the approximation of functions having derivatives of bounded variation.

A completely bounded bilinear operator φ: M×M → M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operators ψj , θj : M → M such that

The Euler and Navier–Stokes equations for an incompressible fluid in two dimensions with periodic boundary conditions are considered. Concerning the Euler equation, previous works analyzed the associated (first order) Liouville operator L as a symmetric linear operator in a Hilbert space L2( ) with respect to a natural invariant Gaussian measure (given by the enstrophy), with domain the subspac...

1σ(T ) is defined to be the set of λ ∈ C such that v 7→ Tv − λv is not a bijection. It is a fact that if T ∈ B(H) and v 7→ Tv − λv is a bijection then it is an element of B(H). That it is linear can be proved quickly. The fact that it is bounded is proved using the open-mapping theorem, which states that a surjective bounded linear map from one Banach space to another is an open map, from which...