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On operator amenability of Fourier-Stieltjes algebras

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Nico Spronk

Operator Algebras · Submitted 21 Jun 2018

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

The authors' main claim In the case that G is connected, we show that operator amenability of B(G) entails that $G$ is compact.

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arXiv ID1806.08421 (version 1)
Pith IDNV3T47JX, Pith's permanent record of this paper and its review
CitationNico Spronk. "On operator amenability of Fourier-Stieltjes algebras." arXiv:1806.08421 (2018). https://pith.science/paper/NV3T47JX
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,905 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 0.43 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G is connected, we show that operator amenability of B(G) entails that $G$ is compact.

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 consider the Fourier-Stietljes algebra B(G) of a locally compact group G. background 0.94 0.22 0.02 asserted 0.58
s1 We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. result 1.00 0.94 0.38 asserted 1.00
s2 In the case that G is connected, we show that operator amenability of B(G) entails that $G$ is compact. result 1.00 0.94 0.40 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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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G is connected, we show that operator amenability of B(G) entails that $G$ is compact.

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