Quantized calculus for perturbed massive Dirac operator on noncommutative Euclidean space

Galina Levitina; Fedor A Sukochev

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

Quantized calculus for perturbed massive Dirac operator on noncommutative Euclidean space

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

Abstract

In this paper we study quantised calculus for the massive unperturbed Dirac operator 𝑚 , m > 0, as well as perturbed Dirac operator 𝑚+𝑉 , on the noncommutative Euclidean space . We prove a necessary and sufficient condition for the quantised derivative 𝑖[sgn(𝑚+𝑉),1⊗𝑥] to belong to the weak Schatten ideal 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
Editors	Pablo Miranda,Nicolas Popoff,Georgi Raikov
Place of Publication	Chile
Publisher	Springer
Pages	179–198
ISBN (Print)	9783030555559
DOIs	https://doi.org/10.1007/978-3-030-55556-6_10
Publication status	Published - 2020
Event	Spectral Theory and Mathematical Physics - Santiago, Chile Duration: 1 Jan 2020 → …

Conference

Conference	Spectral Theory and Mathematical Physics
Country/Territory	Chile
Period	1/01/20 → …
Other	2018

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

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title = "Quantized calculus for perturbed massive Dirac operator on noncommutative Euclidean space",

abstract = "In this paper we study quantised calculus for the massive unperturbed Dirac operator 푚 , m > 0, as well as perturbed Dirac operator 푚+푉 , on the noncommutative Euclidean space . We prove a necessary and sufficient condition for the quantised derivative 푖[sgn(푚+푉),1⊗푥] to belong to the weak Schatten ideal 푑,∞ . This extends and generalises earlier results for Dirac operator on the classical Euclidean space",

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year = "2020",

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

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editor = "{Pablo Miranda,Nicolas Popoff,Georgi Raikov}",

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AU - Sukochev, Fedor A

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N2 - In this paper we study quantised calculus for the massive unperturbed Dirac operator 푚 , m > 0, as well as perturbed Dirac operator 푚+푉 , on the noncommutative Euclidean space . We prove a necessary and sufficient condition for the quantised derivative 푖[sgn(푚+푉),1⊗푥] to belong to the weak Schatten ideal 푑,∞ . 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 푚 , m > 0, as well as perturbed Dirac operator 푚+푉 , on the noncommutative Euclidean space . We prove a necessary and sufficient condition for the quantised derivative 푖[sgn(푚+푉),1⊗푥] to belong to the weak Schatten ideal 푑,∞ . This extends and generalises earlier results for Dirac operator on the classical Euclidean space

U2 - 10.1007/978-3-030-55556-6_10

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

M3 - Conference contribution

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BT - Spectral Theory and Mathematical Physics

A2 - null, Pablo Miranda,Nicolas Popoff,Georgi Raikov

PB - Springer

CY - Chile

T2 - Spectral Theory and Mathematical Physics

Y2 - 1 January 2020

ER -

Quantized calculus for perturbed massive Dirac operator on noncommutative Euclidean space

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