S-spectrum and numerical range of a quaternionic operator
Lu\'is Carvalho, Cristina Diogo, S\'ergio Mendes
TL;DR
This paper explores the relationship between the S-spectrum and the numerical range of bounded linear operators on quaternionic Hilbert spaces, introducing complex operators and characterizing the upper bild of normal operators.
Contribution
It introduces the class of complex operators on quaternionic Hilbert spaces and characterizes the upper bild of normal complex operators in this setting.
Findings
Established the relation between the S-spectrum and numerical range.
Characterized the upper bild of normal complex operators.
Introduced a new class of complex operators on quaternionic Hilbert spaces.
Abstract
We study the numerical range of bounded linear operators on quaternionic Hilbert spaces and its relation with the S-spectrum. The class of complex operators on quaternionic Hilbert spaces is introduced and the upper bild of normal complex operators is completely characterized in this setting.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic and Geometric Analysis · Advanced Topics in Algebra · Matrix Theory and Algorithms