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In this paper, we investigate the Gustafson, Weidmann, Kato, Wolf, Schechter and Browder essential spectra of a 2×2 block matrix operator defined on a Banach space where entries are unbounded operators between Banach spaces and with domains consisting of vectors satisfying certain relations between their components under some properties. Furthermore, we give an application to two-group transport equation.

The electric and dielectric properties of La0.5Ca0.5−xAgxMnO3 (LCMO–Ag with x = 0 and x = 0.4) were investigated using the impedance spectroscopy technique.

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This paper gives a survey on some recent results on the spectral theory of block operator matrices. We study the closeness in the product space and we give some conditions to characterize the essential spectra in the Browder resolvent set case. Furthermore, we apply the obtained results to several models such as delay equations, Sturm-Liouville problem and transport equations.

In this paper a new concept for a 3 × 3 block operator matrix is studied on a Banach space.It is shown that, under certain conditions, it defines a closable operator and its essential spectra are determined. Application to transport operators in L 1 -space is given.

Manganese-based perovskite oxides have attracted much attention since the phenomenon of colossal magnetoresistance (CMR) was revived, where the magnetoresistance (MR) can attend higher orders of magnitude larger than that typically found in other types of materials. While trying to understand the mechanism behind CMR, morphostructural, magnetoelectrical, and theoretical studies have been performed on the La 0.4 Ag 0.2 Ca 0.4 MnO 3 (LACMO) sample. An orthorhombic-shaped singlephase LACMO sample with size distribution D SEM = 2.5 μm was synthesized using a conventional sol−gel chemical method. The mixed valence states of different chemical elements were revealed by X-ray photoemission spectroscopy. The results of thermal dependence of magnetization were obtained according to the zero field cooled−field cooled cooling−field cooled warming protocols using a superconducting quantum interference device magnetometer. The phase separation (PS) phenomenon was observed because of the competition between the superexchange and the double-exchange (DE) mechanisms within the same material. Field dependence of magnetization at varying temperatures and in cooling−warming processes has also been reported and discussed in this paper. The MR value was found to be 99% under an applied field of 2 T. In essence, the reported CMR arises from the metal−insulator phase transition T ρ = 64 K, which accompanies the transition from an insulator state to a metallic state. Not only the large CMR value was noted in our sample, but also the high obtained value of the temperature coefficient of resistivity of 69% at 123 K in zero field has also been reported. The obtained CMR values are the result of PS and multi-DE phenomenon. The latter proved to be directly correlated with the improved magnetotransport properties because an additional hopping mechanism is provided by an interstitially filled Mn 2+ ion, which is electronically involved in the conduction mechanism, showing an unconventional behavior in the transport properties of manganite.