Reversibility is a concept widely studied in several research fields. Several contributions have been provided in physics and computer science. Reversible computation is characterized by means of invertible properties [1]. Reversibility is studied in computer science also in order to design less dissipative computers. The evolution of quantum systems is described by the time evolution operator ...

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

Reversibility is a concept widely studied in physics as well as in computer science. Reversible computation is characterized by means of invertible properties [1]. Quantum systems evolution is described by the time evolution operator U , which is unitary and invertible; therefore such systems can implement reversibility. Reversible/invertible Cellular Automata (CA) [1] are one of the most relev...

We define a minimal relation L0 generated by an integral equation with operators measures and give description of the relations L0- ?E, L*0- where L*0 is adjoint for L0, ?? C. The obtained results are applied to T(?) such that ?E ? T-1(?) bounded everywhere defined operators.

Abstract For any $r\in [0,1]$ we give an example of a rigid operator whose spectrum is the annulus $\{\lambda\in \mathbb{C} : r \le |\lambda| 1 \} $ . In particular, when $r=0$ this and non-invertible, {\kern1pt}] 0,1 [ invertible but its inverse not rigid. This answers two questions Costakis, Manoussos Parissis [Recurrent linear operators. Complex Anal. Oper. Theory 8 (2014), 1601–1643].

In this paper, we investigate the perturbation of the generalized Drazin invertible matrices and derive explicit generalized Drazin inverse expressions for the perturbations under certain restrictions on the perturbing matrices.