On the adjoint of bounded operators in a semi-inner product space R. Respitawulan, Q.Y. Pangestu, E. Kusniyanti, F. Yuliawan, P. Astuti
Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
Abstract
The notion of semi-inner product (SIP) spaces is a generalization of inner product (IP) spaces notion by reducing the positive definite property of the product to positive semi-definite. Hence, it is natural to question which properties, results and characterizations of IP spaces that can be generalized to SIP spaces. In this article we are interested in investigating the adjoint of linear operators on SIP spaces. As in IP spaces, the existence of an adjoint of a linear operator on a SIP space is guaranteed when the operator is bounded. However, in contrast, a bounded linear operator on SIP space can have more than one adjoint linear operators. In this article we give an alternative proof of those results using the generalized Riesz Representation Theorem in SIP space. Further, the description of all adjoint operators of a bounded operator in SIP space will be identified.
