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Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability

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Eva A. Gallardo-Gutiérrez, F. Javier González-Doña

Functional Analysis · Submitted 28 Feb 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces.

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arXiv ID2502.20912 (version 1)
Pith IDWSQSUHV7, Pith's permanent record of this paper and its review
CitationEva A. Gallardo-Guti\'errez, F. Javier Gonz\'alez-Do\~na. "Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability." arXiv:2502.20912 (2025). https://pith.science/paper/WSQSUHV7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,321 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. Moreover, a large subclass consists of decomposable operators in the sense of Colojoar\u{a} and Foia\c{s}.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. result 0.94 0.96 0.92 asserted 1.00
s1 Moreover, a large subclass consists of decomposable operators in the sense of Colojoar\u{a} and Foia\c{s}. result 0.97 0.86 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. Moreover, a large subclass consists of decomposable operators in the sense of Colojoar\u{a} and Foia\c{s}.

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