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On $A$-parallelism and $A$-Birkhoff-James orthogonality of operators
- Publication Year :
- 2020
-
Abstract
- In this paper, we establish several characterizations of the $A$-parallelism of bounded linear operators with respect to the seminorm induced by a positive operator $A$ acting on a complex Hilbert space. Among other things, we investigate the relationship between $A$-seminorm-parallelism and $A$-Birkhoff-James orthogonality of $A$-bounded operators. In particular, we characterize $A$-bounded operators which satisfy the $A$-Daugavet equation. In addition, we relate the $A$-Birkhoff-James orthogonality of operators and distance formulas and we give an explicit formula of the center mass for $A$-bounded operators. Some other related results are also discussed.<br />Comment: 25 pages
- Subjects :
- Mathematics - Functional Analysis
47B65, 47A12, 46C05, 47A05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2007.00179
- Document Type :
- Working Paper