2019/05/02 by Sasmita Patnaik, Patnaik, Sasmita, Srdjan Petrović +4
Computer Science · Mathematics · #47 and 47A65 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.FA #math.OA #msc:47 #msc:47A65
paper · pdf · doi:10.48550/arxiv.1905.00823
8 Pages
openalex publication_date 2019/05/02 · arxiv created 2019/11/04 · arxiv updated 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For H a separable infinite dimensional complex Hilbert space, we prove that every B(H) operator has a basis with respect to which its matrix representation has a universal block tridiagonal form with block sizes given by a simple exponential formula independent of the operator. From this, such a matrix representation can be further sparsified to slightly sparser forms; it can lead to a direct sum of even sparser forms reflecting in part some of its reducing subspace structure; and in the case of operators without invariant subspaces (if any exists), it gives a plethora of sparser block tridiagonal representations. An extension to unbounded operators occurs for a certain domain of definition condition. Moreover this process gives rise to many different choices of block sizes.