2009/01/25 by Yun-Su Kim, Kim, Yun-Su
Computer Science · Mathematics · #47A15 #47S99 #FOS: Mathematics #General Mathematics (math.GM) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.GM #msc:47A15 #msc:47S99
paper · pdf · doi:10.48550/arxiv.0901.3852
openalex publication_date 2009/01/25 · arxiv created 2009/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, to solve the invariant subspace problem, contraction operators are classified into three classes ; (Case 1) completely non-unitary contractions with a non-trivial algebraic element, (Case 2) completely non-unitary contractions without a non-trivial algebraic element, or (Case 3) contractions which are not completely non-unitary. We know that every operator of (Case 3) has a non-trivial invariant subspace. In this paper, we answer to the invariant subspace problem for the operators of (Case 2). Since (Case 1) is simpler than (Case 2), we leave as a question.