Functions of almost commuting operators and an extension of the Helton–Howe trace formula

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Functions of almost commuting operators and an extension of the Helton–Howe trace formula. / Peller, V. V.; Александров, Алексей Борисович.

In: Journal of Functional Analysis, Vol. 271, No. 11, 01.12.2016, p. 3300-3322.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{606f274230084c9a9df10d2bf79cfc0e,

title = "Functions of almost commuting operators and an extension of the Helton–Howe trace formula",

abstract = "Let A and B be almost commuting (i.e., the commutator AB−BA belongs to trace class) self-adjoint operators. We construct a functional calculus φ↦φ(A,B) for functions φ in the Besov class B∞,11(R2). This functional calculus is linear, the operators φ(A,B) and ψ(A,B) almost commute for φ,ψ∈B∞,11(R2), and φ(A,B)=u(A)v(B) whenever φ(s,t)=u(s)v(t). We extend the Helton–Howe trace formula for arbitrary functions in B∞,11(R2). The main tool is triple operator integrals with integrands in Haagerup-like tensor products of L∞ spaces.",

keywords = "Almost commuting operators, Haagerup-like tensor products, Helton–Howe trace formula, Triple operator integrals",

author = "Peller, {V. V.} and Александров, {Алексей Борисович}",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = dec,

day = "1",

doi = "10.1016/j.jfa.2016.09.004",

language = "English",

volume = "271",

pages = "3300--3322",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "11",

}

RIS

TY - JOUR

T1 - Functions of almost commuting operators and an extension of the Helton–Howe trace formula

AU - Peller, V. V.

AU - Александров, Алексей Борисович

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let A and B be almost commuting (i.e., the commutator AB−BA belongs to trace class) self-adjoint operators. We construct a functional calculus φ↦φ(A,B) for functions φ in the Besov class B∞,11(R2). This functional calculus is linear, the operators φ(A,B) and ψ(A,B) almost commute for φ,ψ∈B∞,11(R2), and φ(A,B)=u(A)v(B) whenever φ(s,t)=u(s)v(t). We extend the Helton–Howe trace formula for arbitrary functions in B∞,11(R2). The main tool is triple operator integrals with integrands in Haagerup-like tensor products of L∞ spaces.

AB - Let A and B be almost commuting (i.e., the commutator AB−BA belongs to trace class) self-adjoint operators. We construct a functional calculus φ↦φ(A,B) for functions φ in the Besov class B∞,11(R2). This functional calculus is linear, the operators φ(A,B) and ψ(A,B) almost commute for φ,ψ∈B∞,11(R2), and φ(A,B)=u(A)v(B) whenever φ(s,t)=u(s)v(t). We extend the Helton–Howe trace formula for arbitrary functions in B∞,11(R2). The main tool is triple operator integrals with integrands in Haagerup-like tensor products of L∞ spaces.

KW - Almost commuting operators

KW - Haagerup-like tensor products

KW - Helton–Howe trace formula

KW - Triple operator integrals

UR - http://www.scopus.com/inward/record.url?scp=84995612338&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2016.09.004

DO - 10.1016/j.jfa.2016.09.004

M3 - Article

AN - SCOPUS:84995612338

VL - 271

SP - 3300

EP - 3322

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 11

ER -

ID: 87308468