Some Properties of Cone Inner Product Spaces over Banach Algebra
Anas Yusuf *
Department of Mathematics, Federal University, Birnin Kebbi, Nigeria.
Abor Isa Garba
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The aim of this paper is to introduce a concept of a cone inner product space over Banach algebras. This is done by replacing the co-domain of the classical inner product space by an ordered Banach algebra. Some properties such as Cauchy-Schwarz inequality, parallelogram identity and Pythagoras theorem are established in this setting. Similarly, the notion of cone normed algebra was introduced. Some illustrative examples are given to support our findings.
Keywords: Inner product space, cone inner product space, cone normed space, cone normed algebra, banach algebra.