Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space

Galina Levitina; Fedor A Sukochev

doi:10.1007/978-3-030-55556-6_10

Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space

Galina Levitina
, Fedor A Sukochev

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

Abstract

In this paper we study quantised calculus for the massive unperturbed Dirac operator D_m, m > 0, as well as perturbed Dirac operator D_m + V on the noncommutative Euclidean space L_∞(R_θ^d). We prove a necessary and sufficient condition x ∈ L_∞(R_θ^d) for the quantised derivative i [sgn(D_m + V), 1 ⊗ x ] to belong to the weak Schatten ideal L_d,_∞. This extends and generalises earlier results for Dirac operator on the classical Euclidean space.

Original language	English
Title of host publication	Spectral Theory and Mathematical Physics
Subtitle of host publication	STMP 2018, Santiago, Chile
Editors	Pablo Miranda, Nicolas Popoff, Georgi Raikov
Place of Publication	Cham
Publisher	Springer
Pages	179–198
ISBN (Electronic)	978-3-030-55556-6
ISBN (Print)	978-3-030-55555-9
DOIs	https://doi.org/10.1007/978-3-030-55556-6_10
Publication status	Published - 2020
Event	2018 Spectral Theory and Mathematical Physics International Conference - Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile Duration: 3 Dec 2018 → 7 Dec 2018 https://www.mat.uc.cl/~graikov/conf2018.html (Conference website) https://www.springer.com/gp/book/9783030555559 (Conference proceedings)

Publication series

Name	Latin American Mathematics Series (LAMS)
Publisher	Springer
ISSN (Print)	2524-6755
ISSN (Electronic)	2524-6763

Conference

Conference	2018 Spectral Theory and Mathematical Physics International Conference
Abbreviated title	STMP 2018
Country/Territory	Chile
City	Santiago
Period	3/12/18 → 7/12/18
Internet address	https://www.mat.uc.cl/~graikov/conf2018.html (Conference website) https://www.springer.com/gp/book/9783030555559 (Conference proceedings)

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10.1007/978-3-030-55556-6_10

Cite this

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title = "Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space",

abstract = "In this paper we study quantised calculus for the massive unperturbed Dirac operator Dm , m > 0, as well as perturbed Dirac operator Dm + V on the noncommutative Euclidean space L∞(Rθd). We prove a necessary and sufficient condition x ∈ L∞(Rθd) for the quantised derivative i [sgn(Dm + V), 1 ⊗ x ] to belong to the weak Schatten ideal Ld,∞. This extends and generalises earlier results for Dirac operator on the classical Euclidean space.",

author = "Galina Levitina and Sukochev, \{Fedor A\}",

year = "2020",

doi = "10.1007/978-3-030-55556-6\_10",

language = "English",

isbn = "978-3-030-55555-9",

series = "Latin American Mathematics Series (LAMS)",

publisher = "Springer",

pages = "179–198",

editor = "Pablo Miranda and Nicolas Popoff and Georgi Raikov",

booktitle = "Spectral Theory and Mathematical Physics",

address = "Germany",

note = "2018 Spectral Theory and Mathematical Physics International Conference , STMP 2018 ; Conference date: 03-12-2018 Through 07-12-2018",

url = "https://www.mat.uc.cl/\textasciitilde{}graikov/conf2018.html, https://www.springer.com/gp/book/9783030555559",

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Levitina, G & Sukochev, FA 2020, Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space. in P Miranda, N Popoff & G Raikov (eds), Spectral Theory and Mathematical Physics: STMP 2018, Santiago, Chile. Latin American Mathematics Series (LAMS), Springer, Cham, pp. 179–198, 2018 Spectral Theory and Mathematical Physics International Conference , Santiago, Chile, 3/12/18. https://doi.org/10.1007/978-3-030-55556-6_10

Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space. / Levitina, Galina; Sukochev, Fedor A.
Spectral Theory and Mathematical Physics: STMP 2018, Santiago, Chile. ed. / Pablo Miranda; Nicolas Popoff; Georgi Raikov. Cham: Springer, 2020. p. 179–198 (Latin American Mathematics Series (LAMS)).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

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AU - Levitina, Galina

AU - Sukochev, Fedor A

PY - 2020

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N2 - In this paper we study quantised calculus for the massive unperturbed Dirac operator Dm , m > 0, as well as perturbed Dirac operator Dm + V on the noncommutative Euclidean space L∞(Rθd). We prove a necessary and sufficient condition x ∈ L∞(Rθd) for the quantised derivative i [sgn(Dm + V), 1 ⊗ x ] to belong to the weak Schatten ideal Ld,∞. This extends and generalises earlier results for Dirac operator on the classical Euclidean space.

AB - In this paper we study quantised calculus for the massive unperturbed Dirac operator Dm , m > 0, as well as perturbed Dirac operator Dm + V on the noncommutative Euclidean space L∞(Rθd). We prove a necessary and sufficient condition x ∈ L∞(Rθd) for the quantised derivative i [sgn(Dm + V), 1 ⊗ x ] to belong to the weak Schatten ideal Ld,∞. This extends and generalises earlier results for Dirac operator on the classical Euclidean space.

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DO - 10.1007/978-3-030-55556-6_10

M3 - Conference Paper

SN - 978-3-030-55555-9

T3 - Latin American Mathematics Series (LAMS)

SP - 179

EP - 198

BT - Spectral Theory and Mathematical Physics

A2 - Miranda, Pablo

A2 - Popoff, Nicolas

A2 - Raikov, Georgi

PB - Springer

CY - Cham

T2 - 2018 Spectral Theory and Mathematical Physics International Conference

Y2 - 3 December 2018 through 7 December 2018

ER -

Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space

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