Abstract:
For a bounded right linear operators A, in a right quaternionic
Hilbert space V R
H , following the complex formalism, we study the Berbe rian extension A◦, which is an extension of A in a right quaternionic
Hilbert space obtained from V R
H . In the complex setting, the important
feature of the Berberian extension is that it converts approximate point
spectrum of A into point spectrum of A◦. We show that the same is
true for the quaternionic S-spectrum. As in the complex case, we use
the Berberian extension to study some properties of the commutator of
two quaternionic bounded right linear operators.
