Year: 2026
Type: preprint
Abstract: In 1970, P. R. Halmos raised ten open problems on operator theory. The third problem of Halmos is the following: if an intransitive operator has an inverse, is its inverse also intransitive? This question is reduced to the case of conjugate bi-geometric operators in arXiv: 2610.11202. In the framework of conjugate bi-geometric operators, using tools from complex geometry, operator theory, and function theory, this paper gives an affirmative answer to the third problem of Halmos in the following cases: (a) bundle-preserving operator;(b) subexponential growth of operator norms. These two cases cover a large class of operators.
Source: arXiv (Cornell University)
Authors: Ji, Kui, Jiang, Chunlan, Wang, Zhenyue
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221546350