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On the property $(Z_{E_a})$

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Hassan Zariouh

Functional Analysis · Submitted 13 Jan 2016

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

The authors' main claim A characterization of these properties in terms of localized single valued extension property is given, and the perturbation by commuting Riesz operators is also studied.

how it is stated · asserted 1.00 read the record →

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arXiv ID1601.03175 (version 1)
Pith IDSLTWWDUZ, Pith's permanent record of this paper and its review
CitationHassan Zariouh. "On the property $(Z_{E_a})$." arXiv:1601.03175 (2016). https://pith.science/paper/SLTWWDUZ
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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, 2,908 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.17 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The paper introduces the notion of properties $(Z_{\Pi_a})$ and $(Z_{E_a})$ as variants of Weyl's theorem and Browder's theorem for bounded linear operators acting on infinite dimensional Banach spaces. A characterization of these properties in terms of localized single valued extension property is given, and the perturbation by commuting Riesz operators is also studied. Classes of operators are considered as illustrating examples.

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 paper introduces the notion of properties $(Z_{\Pi_a})$ and $(Z_{E_a})$ as variants of Weyl's theorem and Browder's theorem for bounded linear operators acting on infinite dimensional Banach spaces. contribution 0.99 0.88 0.13 asserted 1.00
s1 A characterization of these properties in terms of localized single valued extension property is given, and the perturbation by commuting Riesz operators is also studied. contribution 0.91 0.90 0.37 asserted 1.00
s2 Classes of operators are considered as illustrating examples. contribution 0.70 0.75 0.04 asserted 0.74

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

What was examined, and what was not

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  • references and citing sentences
  • relations to other papers
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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

The paper introduces the notion of properties $(Z_{\Pi_a})$ and $(Z_{E_a})$ as variants of Weyl's theorem and Browder's theorem for bounded linear operators acting on infinite dimensional Banach spaces. A characterization of these properties in terms of localized single valued extension property is given, and the perturbation by commuting Riesz operators is also studied. Classes of operators are considered as illustrating examples.

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