Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...

For abstract operator spaces V and W , a linear map φ : V → W provides another linear map φn : Mn(A) → Mn(B) defined by φn((ai,j)) = (φ(ai,j)) where n = 1, 2, ···. If a sequence {‖φn‖} ∞ n=1 belongs to l , then φ is said to be a completely bounded map. W. Stinespring [7] and W. Arveson [1] started operator space theory related to complete boundedness for a map φ : S → B(K) where S ⊂ B(H) and H ...

where we used the fact that (σ 2 z) = 1 . In general e−iφfn·fσ = 1 cos(φ)− in · nσ sin(φ) Now we consider a system composed of two subsystems H = H1 ⊗H2, each being a two-level system. To describe operators on the two subsystems we normally use the shorthanded notations A ≡ A ⊗ 1 2 and B ≡ 1 1 ⊗B2 and AB ≡ A ⊗B2 . a) What is (σσ) z z ? b) Consider the operator U = e− 1 iσ iσ φ⊗ z e− z : to whic...

In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution (λ, φ) of a nonlocal operator. ∫ Ω K(x, y)φ(y)dy + a(x)φ(x) = −λφ(x), where Ω ⊂ Rn is an open bounded connected set, K a nonnegative kernel and a is continuous. We prove that for the generalised principal ei...

Abstract. This paper is the companion article of [6]. We consider a discrete elliptic equation on the d-dimensional lattice Z with random coefficients A of the simplest type: They are identically distributed and independent from edge to edge. On scales large w. r. t. the lattice spacing (i. e. unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic...

I point out that if one defines the operator UR(t) as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of UR(t) as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator H but an op...

In this paper, we give some elements about agent-oriented relevance. For that, we define a new modal operator R a so that R a φ means that φ is relevant for agent a concerning the request Q. We discuss properties of this new operator, as well as its extensions and limits.

If the Navier-Stokes equations are averaged with a local, spacial convolution type filter, φ = gδ ∗ φ , the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satisfies

I point out that if one defines the operator UR(t) as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of UR(t) as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator H but an op...

Public announcements are used in dynamic epistemic logic to model certain kinds of information change. A formula 〈ψ〉φ represents the statement that after ψ is publicly announced φ will be the case. Sometimes we want to reason about whether it is possible for φ to become true after some announcement. In order to do this an arbitrary public announcement operator ♦ can be added to an epistemic log...