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arXiv · 2512.00227

Semi-inner product and angles in Schatten ideals

Tamara Bottazzi·Cristian Conde
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Abstract

In this paper, we investigate the Schatten $p$-class ideals for $p >1$ as semi-inner product spaces in the sense of Giles and Lumer. Within this framework, we explore several geometric and analytic notions such as Birkhoff-James orthogonality, $p$-parallelism, and related properties that naturally arise when these structures are interpreted through the lens of the associated semi-inner product. Furthermore, we introduce a novel notion of angle adapted to this context, which generalizes and unifies existing angle definitions in normed spaces. Our results contribute to a deeper understanding of the geometry of the $p$-Schatten class and offer new perspectives on operator behavior in semi-inner product spaces.

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Tamara Bottazzi, Cristian Conde. 2025-11-28. Semi-inner product and angles in Schatten ideals. https://arxiv.org/abs/2512.00227

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