In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

In this paper we characterize hypercyclic translation operators on $$B_{0}(\mathcal {H})$$ , the space of all compact linear a Hilbert $$\mathcal {H}$$ . Also, give some sufficient condition for related cosine operator function to be chaotic or topologically transitive.

In this paper we consider the question when an upward directed set of positive ideal-triangularizable operators on a Banach lattice is (simultaneously) ideal-triangularizable. We prove that a majorized upward directed set of ideal-triangularizable positive operators, which are compact or abstract integral operators is ideal-triangularizable. We also prove that a finite subset of an additive sem...

Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most imitate the more familiar linear algebra of finite-dimensional operator theory. In addition, these are of considerable practical value and importance. We prove a spectral theorem for self-adjoint operators with minimal fuss. Thus, we do not invoke broader discussions of properties of spectr...