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math.FA2026
The invariant subspace problem and Rosenblum operators II
Junsheng Fang, Bingzhe Hou, Chunlan Jiang +1
Let be the separable, infinite-dimensional complex Hilbert space. In the first paper of this series, we introduced, by means of the Rosenblum operators, the shift rep…
math.FA2025
The invariant subspace problem and Rosenblum operators I
Junsheng Fang, Bingzhe Hou, Chunlan Jiang +1
Let be an invertible operator. From the 1940's, Gelfand, Hille and Wermer investigated the invariant subspaces of by analyzing the growth of , wh…
math.FA2025
The Jordan decomposition and Kaplansky's second test problem for Hermitian holomorphic vector bundles
Bingzhe Hou, Chunlan Jiang
In 1954, I. Kaplansky proposed three test problems for deciding the strength of structural understanding of a class of mathematical objects in his treatise "Infinite abelian groups…