If (fn) is a sequence of elements of an infinite dimensional Hilbert space H and (en) is an orthonormal basis for H , we define the preframe operator T : H → H by: Ten = fn. It follows that for any f ∈ H , T ∗f = ∑ n〈f, fn〉en. Hence, (fn) is a frame if and only if T ∗ is an isomorphism (called the frame transform) and in this case S = TT ∗ is an invertible operator on H called the frame operato...

If T or T ∗ is an algebraically k-quasiclass A operator acting on an infinite dimensional separable Hilbert space and F is an operator commuting with T , and there exists a positive integer n such that F has a finite rank, then we prove that Weyl’s theorem holds for f(T )+F for every f ∈ H(σ(T )), where H(σ(T )) denotes the set of all analytic functions in a neighborhood of σ(T ). Moreover, if ...

Let (M, F) be a closed foliated manifold, dimM = n, dimF = p, p+q = n, equipped with a Riemannian metric gM . We assume that the foliation F is Riemannian, and the metric gM is bundle-like. Let F = TF be the integrable distribution of tangent p-planes to F , and H = F⊥ be the orthogonal complement to F . The decomposition of TM into a direct sum, TM = F ⊕ H , induces a decomposition of the metr...

In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point p...

The idea of difference sequences of real (or complex) numbers was introducedby Ki zmaz cite{Kizmaz}. In this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  Delta,mathcal{F}right)  .$ We study some of its properties likesolidity, symmetricity, etc.

In this paper we study weighted composition operators on Orlicz spaces. Introduction : Let X and Y be two non empty sets and let F(X) and F(Y) be denoted the topological vector spaces of complex valued functions on X and Y respectively. If T : Y → X is a mapping such that f oT ∈ F (Y) whenever f ∈ F (X), then we can define a composition transformation C T : F (X) → F (Y) by C T f = f oT for eve...

We calculate the nucleon matrix element of Weinberg's dimension-6 CP-odd gluon operator fabc(F˜??)a(F??)b(F??)c in instanton vacuum. In leading order packing fraction, is effectively proportional to topological charge density (F˜??)a(F??)a, whose given by flavor-singlet axial and constrained U(1)A anomaly. The obtained substantially larger than other estimates, because strong localization nonpe...

Let F (u ε) + ε(u ε − w) = 0 (1) where F is a nonlinear operator in a Hilbert space H, w ∈ H is an element, and ε > 0 is a parameter. Assume that F (y) = 0, and F ′ (y) is not a boundedly invertible operator. Sufficient conditions are given for the existence of the solution to (1.1) and for the convergence lim ε→0 u ε − y = 0. An example of applications is considered. In this example F is a non...

In these lectures, we concentrate on the motivations, development and applications of the Calderon-Zygmund operator theory. Lecture 1. The differential operators with constant coefficients and the first generation of Calderon-Zygmund operators Consider the following differential operator with constant coefficients: Lu(x) = α a α ∂ α u ∂x α. By taking the Fourier transform, (Lu)(ξ) = α a α (−2πi...

Various bounds in the operator order for the following operator transform f̃ (A) := 1 2 [f (A)− f ((m + M) 1H −A)] , where A is a selfadjoint operator in the Hilbert space H with the spectrum Sp (A) ⊆ [m,M ] and f : [m,M ] → C is a continuous function on [m,M ] are given. Applications for the power and logaritmic functions are provided as well.