Some Remarks Concerning Operator Lipschitz Functions

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Some Remarks Concerning Operator Lipschitz Functions. / Александров, Алексей Борисович.

In: Journal of Mathematical Sciences (United States), Vol. 251, No. 2, 01.11.2020, p. 176-189.

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

BibTeX

@article{3f02528aa1e7490ea1cc88d9e77883d0,

title = "Some Remarks Concerning Operator Lipschitz Functions",

abstract = "We consider examples of operator Lipschitz functions f for which the operator Lipschitz seminorm ‖f‖OL(ℝ) coincides with the Lipschitz seminorm ‖f‖Lip(ℝ). In particular, we consider the operator Lipschitz functions f such that |f ' (0)| = ‖f‖OL(ℝ). It is well known that f has this property if its derivative f′ is positive definite. It is proved in this paper that there are other functions having this property. It is also shown that the identity |f ' (t0)| = ‖f‖OL(ℝ) implies the continuity of f at t0. In fact, a more general statement is established concerning commutator Lipschitz functions on a closed subset of the complex plane.",

author = "Александров, {Алексей Борисович}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2020",

month = nov,

day = "1",

doi = "10.1007/s10958-020-05078-4",

language = "English",

volume = "251",

pages = "176--189",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Some Remarks Concerning Operator Lipschitz Functions

AU - Александров, Алексей Борисович

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We consider examples of operator Lipschitz functions f for which the operator Lipschitz seminorm ‖f‖OL(ℝ) coincides with the Lipschitz seminorm ‖f‖Lip(ℝ). In particular, we consider the operator Lipschitz functions f such that |f ' (0)| = ‖f‖OL(ℝ). It is well known that f has this property if its derivative f′ is positive definite. It is proved in this paper that there are other functions having this property. It is also shown that the identity |f ' (t0)| = ‖f‖OL(ℝ) implies the continuity of f at t0. In fact, a more general statement is established concerning commutator Lipschitz functions on a closed subset of the complex plane.

AB - We consider examples of operator Lipschitz functions f for which the operator Lipschitz seminorm ‖f‖OL(ℝ) coincides with the Lipschitz seminorm ‖f‖Lip(ℝ). In particular, we consider the operator Lipschitz functions f such that |f ' (0)| = ‖f‖OL(ℝ). It is well known that f has this property if its derivative f′ is positive definite. It is proved in this paper that there are other functions having this property. It is also shown that the identity |f ' (t0)| = ‖f‖OL(ℝ) implies the continuity of f at t0. In fact, a more general statement is established concerning commutator Lipschitz functions on a closed subset of the complex plane.

UR - http://www.scopus.com/inward/record.url?scp=85093826058&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-05078-4

DO - 10.1007/s10958-020-05078-4

M3 - Article

AN - SCOPUS:85093826058

VL - 251

SP - 176

EP - 189

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 87314630