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The Maxwell operator in a 3D cylinder is considered. The coefficients are assumed to be scalar functions depending on the longitudinal variable only. Such an operator is represented as a sum of a countable set of matrix differential operators of first order acting in $ L_2(\mathbb {R}) $ L 2 (R). Based on this representation we give a detailed description of the structure of the spectrum of the Maxwell operator in two particular cases: (1) in the case of coefficients stabilizing at infinity; and (2) in the case of periodic coefficients. [ABSTRACT FROM AUTHOR]

A bounded linear operator T on a complex Banach space X is superconvex-cyclic, if for some vector x in the space, C. c o (o r b (T , x)) is dense. Here, co(orb(T, x)) means the convex hull of { T n x : n ≥ 0 }. In this paper, we give necessary conditions for the superconvex-cyclicity of an operator in terms of the point spectrum of its adjoint. Also, we prove that positive multiples of superconvex-cyclic operators are superconvex-cyclic. However, this concept is not necessarily transferred to positive integer powers of an operator. Moreover, we completely characterize superconvex-cyclic matrices whose spectra contain no real number or contain a positive real number. [ABSTRACT FROM AUTHOR]

Aq-analog expression of the determinantal polynomial of a weighted shift operator is introduced and applied to find the numerical radius of the operator. [ABSTRACT FROM AUTHOR]

This work consists of two parts. The first one contains a characterization (localization) of the point spectrum of one sided, infinite and periodic Jacobi matrices with scalar entries. The second one deals with the same questions about one sided, infinite periodic Jacobi matrices with matrix entries. In particular, an example illustrating the difference between the above localization property in scalar and matrix entries cases is given. [ABSTRACT FROM AUTHOR]

The spectral properties of the off-diagonal infinite-dimensional Hamiltonian operator are studied in this article. Characterizations of the spectrum, the point spectrum and the residual spectrum are given. A spectral inclusion property of numerical range is proved. [ABSTRACT FROM AUTHOR]