K₀-groups and strongly irreducible decompositions of operator tuples

2024/03/19 by Jing Xu, Xu, Jing
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2403.12348

openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

An operator tuple T=(T₁,…,T_n) is called strongly irreducible (SI), if the joint commutant of 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 K₀-group of the commutant of operator tuples. As an application, we calculate K₀-groups of some multiplier algebras, and describe the similarity of backwards multishifts on Drury-Arveson space by means of inflation theory.

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