What does this research mean for the field?

A new definition of orthogonality in normed spaces, based on ϼ*-orthogonality, exhibits fundamental properties such as symmetry, non-negativity, and scalar homogeneity, and relates systematically to other established types of orthogonality. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The study aims to analyze the fundamental properties of a new type of orthogonality in normed spaces.

June 3, 2026Open Access

New Kind of orthogonality in Normed spaces by using ϼ * -orthogonality.

Key Points

The study aims to analyze the fundamental properties of a new type of orthogonality in normed spaces.
Systematic analysis of properties including symmetry, non-negativity, scalar homogeneity.
Exploration of relationships with existing orthogonality types.
Focus on linear independence of orthogonal vectors and inequalities.
Demonstrated symmetry and non-negativity in the new orthogonality framework.
Established linear independence of orthogonal vectors under the new definition.
Outlined connections to the Cauchy-Schwarz type inequality.

Abstract

-orthogonality. The fundamental properties of this new concept are systematically analyzed, including symmetry, non-negativity, scalar homogeneity, linear independence of orthogonal vectors, the Cauchy-Schwarz type inequality, the zero property, and other characteristics. We also explain the relationship between this new definition and some other well-known types of orthogonality.

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