The iterated Aluthge transform of an operator

Il Bong Jung; Eungil Ko; Carl Pearcy

doi:10.1007/s000200300012

The iterated Aluthge transform of an operator

Il Bong Jung, Eungil Ko, Carl Pearcy

Department of Mathematics

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

36 Scopus citations

Abstract

The Aluthge transform T̃ (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated T̃, and this study was continued in [7], in which relations between the spectral pictures of T and T̃ were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates {T̃⁽ⁿ⁾} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence {T̃⁽ⁿ⁾}converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).

Original language	English
Pages (from-to)	375-387
Number of pages	13
Journal	Integral Equations and Operator Theory
Volume	45
Issue number	4
DOIs	https://doi.org/10.1007/s000200300012
State	Published - 2003

Bibliographical note

Funding Information:
The first author was partially supported by KOSEF Research Project No. R01-2000-00003. The second author was supported by Korea Research Foundation Grant (KRF-2000-015-DP0023). The third author appreciates the support of the National Science Foundation.

Keywords

Aluthge transform
p-hyponormal operator
Quasinilpotent operator
Wighted shift

Access to Document

10.1007/s000200300012

Cite this

@article{b1091e1460cc49fdb166904180184c76,

title = "The iterated Aluthge transform of an operator",

abstract = "The Aluthge transform {\~T} (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated {\~T}, and this study was continued in [7], in which relations between the spectral pictures of T and {\~T} were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates {{\~T}(n)} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence {{\~T}(n)}converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).",

keywords = "Aluthge transform, p-hyponormal operator, Quasinilpotent operator, Wighted shift",

author = "Jung, {Il Bong} and Eungil Ko and Carl Pearcy",

note = "Funding Information: The first author was partially supported by KOSEF Research Project No. R01-2000-00003. The second author was supported by Korea Research Foundation Grant (KRF-2000-015-DP0023). The third author appreciates the support of the National Science Foundation.",

year = "2003",

doi = "10.1007/s000200300012",

language = "English",

volume = "45",

pages = "375--387",

journal = "Integral Equations and Operator Theory",

issn = "0378-620X",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - The iterated Aluthge transform of an operator

AU - Jung, Il Bong

AU - Ko, Eungil

AU - Pearcy, Carl

N1 - Funding Information: The first author was partially supported by KOSEF Research Project No. R01-2000-00003. The second author was supported by Korea Research Foundation Grant (KRF-2000-015-DP0023). The third author appreciates the support of the National Science Foundation.

PY - 2003

Y1 - 2003

N2 - The Aluthge transform T̃ (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated T̃, and this study was continued in [7], in which relations between the spectral pictures of T and T̃ were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates {T̃(n)} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence {T̃(n)}converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).

AB - The Aluthge transform T̃ (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated T̃, and this study was continued in [7], in which relations between the spectral pictures of T and T̃ were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates {T̃(n)} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence {T̃(n)}converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).

KW - Aluthge transform

KW - p-hyponormal operator

KW - Quasinilpotent operator

KW - Wighted shift

UR - http://www.scopus.com/inward/record.url?scp=0037275396&partnerID=8YFLogxK

U2 - 10.1007/s000200300012

DO - 10.1007/s000200300012

M3 - Article

AN - SCOPUS:0037275396

SN - 0378-620X

VL - 45

SP - 375

EP - 387

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -

The iterated Aluthge transform of an operator

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this