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Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators

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Peter Saveliev

Functional Analysis · Submitted 29 Aug 2000

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

The authors' main claim We generalize this theorem for multivalued linear operators.

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arXiv IDmath/0008214 (version 1)
Pith IDMYKYM4NK, Pith's permanent record of this paper and its review
CitationPeter Saveliev. "Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators." arXiv:math/0008214 (2000). https://pith.science/paper/MYKYM4NK
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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.65 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators.

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 The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant subspace. background 1.00 0.03 0.06 asserted 1.00
s1 We generalize this theorem for multivalued linear operators. contribution 0.99 0.93 0.46 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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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

The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators.

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