Operator Lipschitz functions and linear fractional transformations

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Operator Lipschitz functions and linear fractional transformations. / Александров, Алексей Борисович.

In: Journal of Mathematical Sciences (United States), Vol. 194, No. 6, 11.2013, p. 603-627.

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

BibTeX

@article{24617ea07208407b942a82e898b306b3,

title = "Operator Lipschitz functions and linear fractional transformations",

abstract = "It is known that the function (Formula presented.) is an operator Lipschitz function on the real line (Formula presented.). We prove that the function sin can be replaced by any operator Lipschitz function f with f(0) = 0. In other words, for every operator Lipschitz function f, the function (Formula presented.) is also operator Lipschitz if f(0) = 0. The function f can be defined on an arbitrary closed subset of the complex plane (Formula presented.). Moreover, the linear fractional transformation (Formula presented.) can be replaced by every linear fractional transformation φ{symbol}. In this case, we assert that the function (Formula presented.) is operator Lipschitz for every operator Lipschitz function f provided that f(φ{symbol}(∞)) = 0. Bibliography: 12 titles.",

author = "Александров, {Алексей Борисович}",

year = "2013",

month = nov,

doi = "10.1007/s10958-013-1550-z",

language = "English",

volume = "194",

pages = "603--627",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Operator Lipschitz functions and linear fractional transformations

AU - Александров, Алексей Борисович

PY - 2013/11

Y1 - 2013/11

N2 - It is known that the function (Formula presented.) is an operator Lipschitz function on the real line (Formula presented.). We prove that the function sin can be replaced by any operator Lipschitz function f with f(0) = 0. In other words, for every operator Lipschitz function f, the function (Formula presented.) is also operator Lipschitz if f(0) = 0. The function f can be defined on an arbitrary closed subset of the complex plane (Formula presented.). Moreover, the linear fractional transformation (Formula presented.) can be replaced by every linear fractional transformation φ{symbol}. In this case, we assert that the function (Formula presented.) is operator Lipschitz for every operator Lipschitz function f provided that f(φ{symbol}(∞)) = 0. Bibliography: 12 titles.

AB - It is known that the function (Formula presented.) is an operator Lipschitz function on the real line (Formula presented.). We prove that the function sin can be replaced by any operator Lipschitz function f with f(0) = 0. In other words, for every operator Lipschitz function f, the function (Formula presented.) is also operator Lipschitz if f(0) = 0. The function f can be defined on an arbitrary closed subset of the complex plane (Formula presented.). Moreover, the linear fractional transformation (Formula presented.) can be replaced by every linear fractional transformation φ{symbol}. In this case, we assert that the function (Formula presented.) is operator Lipschitz for every operator Lipschitz function f provided that f(φ{symbol}(∞)) = 0. Bibliography: 12 titles.

UR - http://www.scopus.com/inward/record.url?scp=84899028258&partnerID=8YFLogxK

U2 - 10.1007/s10958-013-1550-z

DO - 10.1007/s10958-013-1550-z

M3 - Article

AN - SCOPUS:84899028258

VL - 194

SP - 603

EP - 627

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 87317456