Barbour path functions and related operator means

Noboru Nakamura

doi:10.1016/j.laa.2013.06.035

Barbour path functions and related operator means

Noboru Nakamura

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

1 Citation (Scopus)

Abstract

We consider Barbour path function ^Fx(a,b)=a×bax+ba(1-x) x+ba(1-x) (0≤x≤1, a,b>0) as an approximation of the exponential function (or the geometric mean path) ^Gx(a,b)=a1^-x ^bx (0≤x≤1, a,b>0) by a linear fractional function, which interpolates G_x(a,b) at x=0,12 and 1. If a=1 and b=t, then both the functions F_x(1,t) and G_x(1,t) are operator monotone in t, parameterized with x. We also consider the order relation between the integral mean for the Barbour path function and another mean.

Original language	English
Pages (from-to)	2434-2441
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	439
Issue number	8
DOIs	https://doi.org/10.1016/j.laa.2013.06.035
Publication status	Published - Oct 15 2013
Externally published	Yes

Keywords

Operator mean
Operator monotone function
Path

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2013.06.035

Cite this

@article{8a384e1b176b4aeab56898c1adc9d4d4,

title = "Barbour path functions and related operator means",

abstract = "We consider Barbour path function Fx(a,b)=a×bax+ba(1-x) x+ba(1-x) (0≤x≤1, a,b>0) as an approximation of the exponential function (or the geometric mean path) Gx(a,b)=a1-x bx (0≤x≤1, a,b>0) by a linear fractional function, which interpolates Gx(a,b) at x=0,12 and 1. If a=1 and b=t, then both the functions Fx(1,t) and Gx(1,t) are operator monotone in t, parameterized with x. We also consider the order relation between the integral mean for the Barbour path function and another mean.",

keywords = "Operator mean, Operator monotone function, Path",

author = "Noboru Nakamura",

year = "2013",

month = oct,

day = "15",

doi = "10.1016/j.laa.2013.06.035",

language = "English",

volume = "439",

pages = "2434--2441",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "8",

}

TY - JOUR

T1 - Barbour path functions and related operator means

AU - Nakamura, Noboru

PY - 2013/10/15

Y1 - 2013/10/15

N2 - We consider Barbour path function Fx(a,b)=a×bax+ba(1-x) x+ba(1-x) (0≤x≤1, a,b>0) as an approximation of the exponential function (or the geometric mean path) Gx(a,b)=a1-x bx (0≤x≤1, a,b>0) by a linear fractional function, which interpolates Gx(a,b) at x=0,12 and 1. If a=1 and b=t, then both the functions Fx(1,t) and Gx(1,t) are operator monotone in t, parameterized with x. We also consider the order relation between the integral mean for the Barbour path function and another mean.

AB - We consider Barbour path function Fx(a,b)=a×bax+ba(1-x) x+ba(1-x) (0≤x≤1, a,b>0) as an approximation of the exponential function (or the geometric mean path) Gx(a,b)=a1-x bx (0≤x≤1, a,b>0) by a linear fractional function, which interpolates Gx(a,b) at x=0,12 and 1. If a=1 and b=t, then both the functions Fx(1,t) and Gx(1,t) are operator monotone in t, parameterized with x. We also consider the order relation between the integral mean for the Barbour path function and another mean.

KW - Operator mean

KW - Operator monotone function

KW - Path

UR - http://www.scopus.com/inward/record.url?scp=84882876729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84882876729&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2013.06.035

DO - 10.1016/j.laa.2013.06.035

M3 - Article

AN - SCOPUS:84882876729

VL - 439

SP - 2434

EP - 2441

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 8

ER -

Barbour path functions and related operator means

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this