Quaternionic operators with finite matrix trace

In this paper we consider bounded liner operators in quaternionic Hilbert space, having finite and invariant matrix trace. We prove that any such operator is selfadjoint. Besides, we prove that dual space of the real normed space of all such operators is isomorphic to the Banach space of all selfadjoint operators.This research was supported by Science Fund of Serbia, through the Mathematical Faculty of Belgrade.