In an inner product space, two vectors are orthogonal if their inner product
is zero. In a normed space, numerous notions of orthogonality have been
introduced via equivalent propositions to the usual orthogonality, e.g.
orthogonal vectors satisfy the Pythagorean law. In 2010, Kikianty and
Dragomir [9] introduced the p-HH-norms (1 ? p < ?) on the Cartesian square of
a normed space. Some notions of orthogonality have been introduced by
utilizing the 2-HH-norm [10]. These notions of orthogonality are closely
related to the classical Pythagorean orthogonality and Isosceles
orthogonality. In this paper, a Carlsson type orthogonality in terms of the
2-HH-norm is considered, which generalizes the previous definitions. The main
properties of this orthogonality are studied and some useful consequences are
obtained. These consequences include characterizations of inner product
space.
Circle-Uniqueness of Pythagorean Orthogonality in Normed Linear Spaces
