The decomposition theorems in Baer $*$-rings
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz, Marek S{\l}oci\'nski
TL;DR
This paper generalizes decomposition theorems from bounded Hilbert space operators to Baer *-rings, introducing new results and models for summands, thereby broadening the algebraic framework for operator decompositions.
Contribution
It provides a general decomposition theorem in Baer *-rings and extends known decompositions to this broader algebraic setting, including new results.
Findings
General decomposition theorem in Baer *-rings
Extension of known decompositions to Baer *-rings
New results in the algebra of bounded Hilbert space operators
Abstract
We show a general decomposition theorem in Baer *-rings. As a consequence the vast majority of decompositions known in the algebra of bounded Hilbert space operators are generalized to Baer *-rings. There are also results which are new in the algebra of bounded Hilbert space operators. The model of summands in Wold-S{\l}oci\'nski decomposition in Baer *-rings is given.
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
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Advanced Algebra and Logic