Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2512.00227 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917113509183488 |
|---|---|
| author | Bottazzi, Tamara Conde, Cristian |
| author_facet | Bottazzi, Tamara Conde, Cristian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-inner product and angles in Schatten ideals Bottazzi, Tamara Conde, Cristian Functional Analysis Operator Algebras 46C50 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. |
| title | Semi-inner product and angles in Schatten ideals |
| topic | Functional Analysis Operator Algebras 46C50 |
| url | https://arxiv.org/abs/2512.00227 |