$K_{0}$-groups and strongly irreducible decompositions of operator tuples
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916165797806080 |
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| author | Xu, Jing |
| author_facet | Xu, Jing |
| contents | An operator tuple $\mathbf{T}=(T_{1},\ldots,T_{n})$ is called strongly irreducible (SI), if the joint commutant of $\mathbf{T}$ does not any nontrivial idempotent operator. In this paper, we study the uniqueness of finitely strong irreducible decomposition of operator tuples up to similarity by $K$-theory of operator algebra, and give the algebraically similarity invariants of the Cowen-Douglas tuple with index 1 by using $K_{0}$-group of the commutant of operator tuples. As an application, we calculate $K_{0}$-groups of some multiplier algebras, and describe the similarity of backwards multishifts on Drury-Arveson space by means of inflation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $K_{0}$-groups and strongly irreducible decompositions of operator tuples Xu, Jing Functional Analysis Operator Algebras An operator tuple $\mathbf{T}=(T_{1},\ldots,T_{n})$ is called strongly irreducible (SI), if the joint commutant of $\mathbf{T}$ does not any nontrivial idempotent operator. In this paper, we study the uniqueness of finitely strong irreducible decomposition of operator tuples up to similarity by $K$-theory of operator algebra, and give the algebraically similarity invariants of the Cowen-Douglas tuple with index 1 by using $K_{0}$-group of the commutant of operator tuples. As an application, we calculate $K_{0}$-groups of some multiplier algebras, and describe the similarity of backwards multishifts on Drury-Arveson space by means of inflation theory. |
| title | $K_{0}$-groups and strongly irreducible decompositions of operator tuples |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2403.12348 |