Several representations of the generalized Drazin inverse of a block matrix with a group invertible generalized Schur complement in Banach algebra are presented.

Given a bounded operator A on a Banach space X with Drazin inverse A and index r, we study the class of group invertible bounded operators B such that / + A (B — A) is invertible and 1Z(B) f]N(A) = {0}. We show that they can be written with respect to the decomposition X = lZ(A) 0 Af(A) as a matrix operator, B = ( _ _ __i _ ), where B\ and B\ + B\9#?1 a r e invertible. ^ if21 t>2\tf\ i*\2 Sever...

The possibility is investigated that a nonlocal formulation of gauge theories may provide an alternative mechanism for the generation of mass. For this purpose, a path-integral approach is used, with gauge-averaging term leading to an invertible integro-differential operator on field disturbances and to a mass term in the semiclassical Lagrangian. It is therefore shown that suitable choices of ...

For a given standard Hamiltonian H = [p − A(x)]2/(2m) + V (x) with arbitrary complex scalar potential V and vector potential A, with x ∈ R, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT -symmetric Hamiltonian wi...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

We present some new representations for the generalized Drazin inverse of a block matrix with generalized Schur complement being generalized Drazin invertible in a Banach algebra under conditions weaker than those used in recent papers on the subject.

Abstract. The purpose of this note is to give explicit criteria to determine whether a real generalized Cartan matrix is of finite type, affine type or of hyperbolic type by considering the principal minors and the inverse of the matrix. In particular, it will be shown that a real generalized Cartan matrix is of finite type if and only if it is invertible and the inverse is a positive matrix. A...

The possibility is investigated that a nonlocal formulation of gauge theories may provide an alternative mechanism for the generation of mass. For this purpose, a path-integral approach is used, with gauge-averaging term leading to an invertible integro-differential operator on field disturbances and to a mass term in the semiclassical Lagrangian. It is therefore shown that suitable choices of ...