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Asymmetric truncated Toeplitz operators on finite-dimensional spaces

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Joanna Jurasik, Bartosz {L}anucha

Functional Analysis · Submitted 2 Nov 2016

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

The authors' main claim Our results are generalizations of the results known for truncated Toeplitz operators.

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arXiv ID1611.00813 (version 1)
Pith IDAVSZ7YH6, Pith's permanent record of this paper and its review
CitationBartosz {\L}anucha, Joanna Jurasik. "Asymmetric truncated Toeplitz operators on finite-dimensional spaces." arXiv:1611.00813 (2016). https://pith.science/paper/AVSZ7YH6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,439 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.38 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. Our results are generalizations of the results known for truncated Toeplitz 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 In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. contribution 0.75 0.62 0.05 asserted 0.91
s1 We compute the dimension of the space of all such operators. result 0.80 0.96 0.29 asserted 1.00
s2 We also describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. contribution 0.77 0.94 0.16 asserted 1.00
s3 Our results are generalizations of the results known for truncated Toeplitz operators. interpretation 0.92 0.47 0.20 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

In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. Our results are generalizations of the results known for truncated Toeplitz operators.

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1 arXiv paper cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper
  • A characterization of operators form $𝒯(α,β)$ in terms of compressed shifts was obtained in [ref] for $α$ and $β$ such that $β$ divides $α$ ($α/β$ is also an inner function), whereas the matrix representations of asymmetric truncated Toeplitz operators on finite-dimensional spaces were discussed in [ref] .

    Asymmetric truncated Toeplitz operators on finite-dimensional spaces II · Introduction · 0.85

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