Additive maps preserving the reduced minimum modulus of Banach space operators

Let ${\mathcal B}(X)$ be the algebra of all bounded linear operators on an infinite dimensional complex Banach space $X$. We prove that an additive surjective map $\phi$ on ${\mathcal B}(X)$ preserves the reduced minimum modulus if and only if either there are bijective isometries $U:X\to X$ and $V:X\to X$ both linear or both conjugate linear such that $\phi(T)=UTV$ for all $T\in{\mathcal B}(X)$, or $X$ is reflexive and there are bijective isometries $U:X^*\to X$ and $V:X\to X^*$ both linear or both conjugate linear such that $\phi(T)=UT^*V$ for all $T\in{\mathcal B}(X)$. As immediate consequences of the ingredients used in the proof of this result, we get the complete description of surjective additive maps preserving the minimum, the surjectivity and the maximum moduli of Banach space operators.Comment: The abstract of this paper was posted on May 2009 in the web page of the analysis group of Laval University (http://newton.mat.ulaval.ca/analyse/abstracts/2009-06.pdf

Bounded Point Evaluations and Local Spectral Theory

We study in this paper the concept of bounded point evaluations for cyclic operators. We give a negative answer to a question of L.R. Williams {\it Dynamic Systems and Apllications} 3(1994) 103-112. Furthermore, we generalize some results of Williams and give a simple proof of theorem 2.5 of L.R. Williams (The Local Spectra of Pure Quasinormal Operators J. Math. anal. Appl. 187(1994) 842-850) that non normal hyponormal weighted shifts have fat local spectra.Comment: 44pp, diploma thesi

The single-valued extension property for bilateral operator weighted shifts

In this paper, we give necessary and sufficient conditions for a bilateral operator weighted shift to enjoy the single-valued extension property

Maps preserving the local spectrum of quadratic products of matrices

Let Mn(C) denote the algebra of all n × n complex matrices, and fix a nonzero vector x0 in C n . For any matrix T ∈ Mn(C), let σT (x0) denote the local spectrum of T at x0. Given three scalars µ, ν and ξ simultaneously nonzero, we study maps ϕ on Mn(C) satisfying σµST S+νT S+ξST (x0) = σµϕ(S)ϕ(T )ϕ(S)+νϕ(T )ϕ(S)+ξϕ(S)ϕ(T )(x0) for all S, T ∈ Mn(C). Our main result extends and unifies the main results of several papers on maps on Mn(C) preserving the local spectrum of different products

On the largest analytic set for cyclic operators

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Melanogenesis Promoting Effect, Antioxidant Activity, and UPLC-ESI-HRMS Characterization of Phenolic Compounds of Argan Leaves Extract

The use of natural products for the regulation of skin pigmentation is gaining popularity. In the present study, we evaluated the effect of argan leaves extract (ALE) on melanogenesis in B16 melanoma cells, determined its antioxidant activity, then quantified and identified its phenolic components. B16 cells were treated with various concentrations of ALE, then the cell viability and proliferation were assessed using MTT assay while the melanin content was determined using spectrophotometric methods. The expression level of tyrosinase (TYR), tyrosinase related protein-1 (TRP-1) and dopachrome tautomerase (DCT) was evaluated by Western blotting. The antioxidant activity of ALE was investigated using four different assays while UPLC-ESI-HRMS analysis was used to characterize the ALE phenolic profile. Fourteen phenolic compounds were identified, of which six are reported for the first time to be present in ALE. ALE treatment increases the melanin content of B16 cells in a dose-dependent manner without cytotoxicity. This was revealed by the observed ALE-increased expression level of TYR, DCT, and TRP-1. These bioactivities may be mainly attributed to its high flavonoids content. Argan leaves have the potential for use as a treatment for hypopigmentation disorders and as a bioactive component of cosmetic products that aim to increase pigmentation