Let A be a C-algebra acting on a Hilbert space H, σ : A → B(H) be a linear mapping and d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous ∗-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous ∗-σ-derivation then there exists a continuous linear mapping Σ : A → B...

Let A be a C-algebra acting on a Hilbert space H, σ : A → B(H) be a linear mapping and d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous ∗-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous ∗-σ-derivation then there exists a continuous linear mapping Σ : A → B...

Motivated by the recent successful results of using GIS modeling in a variety of problems related to the geosciences, some knowledge-based methods were applied to a regional scale mapping of the mineral potential, special for Cu-Au mineralization in the Feyz-Abad area located in the NE of Iran. Mineral Prospectivity Mapping (MPM) is a multi-step process that ranks a promising target area for mo...

Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range. Throughout this paper, we assume that X is a real Hilbert space, with inner product p = 〈· | ·〉 and induced norm...

Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on was first defined and topologized by the author. In this article, we give explicit description topology using coordinates. More precisely, given every point in space, find continuous coordinates quotient a suitable open neighborhood about subgroup ma...

Let E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...

We exhibit a locally biholomorphic mapping with simply connected image, which fails to be a topological covering. Introduction In [1], A.F.Beardon shows an example of a ’covering surface’ over the unit disc D ⊂ C, which is not a topological covering. We recall that a ’covering surface’ of a regionD ⊂ C, is a Riemann surface S admitting surjective conformal mapping onto D, whereas a continuous m...

Twenty nine patients (aged from three months to 37 years) with confirmed or suspected ventricular septal defects were studied separately by three examiners who used colour flow mapping and imaging, or continuous wave Doppler and imaging, or a combined reference examination. Colour flow mapping identified 19 of the 25 patients with a ventricular septal defect, continuous wave Doppler echocardiog...

The Fixed Point Theorem had been proved on Reciprocally Continuous Self Mapping. In this paper the fixed point theorem on reciprocally continuous self mapping is proved under Menger Space.