On Consistent Operators and Reflexivity

被引：3

作者：

Azoff, Edward A. ^{[5
]}

Li, Wing Suet ^{[4
]}

Mbekhta, Mostafa ^{[3
]}

Ptak, Marek ^{[1
,2
]}

机构：

[1] Univ Agr, Inst Math, PL-30198 Krakow, Poland

[2] Pedag Univ, Inst Math, PL-30084 Krakow, Poland

[3] Univ Lille 1, UFR Math, CNRS, UMR 8524, F-59655 Villeneuve Dascq, France

[4] Georgia Inst Technol, Dept Math, Atlanta, GA 30332 USA

[5] Univ Georgia, Dept Math, Athens, GA 30602 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2011年 / 71卷 / 01期

基金：

美国国家科学基金会;

关键词：

Reflexive algebra; direct sum of shifts; isometry; linear order; power partial isometry; LINEAR TRANSFORMATIONS; ALGEBRAS;

D O I：

10.1007/s00020-011-1894-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Hilbert space operators A = circle plus(i is an element of N)A(i) which are consistent in the sense that each A (i+1) contains a copy of A (i) . The formal definition is reminiscent of the classical ordering on projections in a von Neumann algebra. It is shown that if the powers of A are simultaneously consistent, then A must be reflexive. This is applied to study reflexivity of power partial isometries.

引用

页码：1 / 12

页数：12

共 19 条

[1] AZOFF E, 1986, MEM AM MATH SOC, V357
[2] On rank two linear transformations and reflexivity
Azoff, EA
Ptak, M
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1996, 53 : 383 - 396
[3] A dichotomy for linear spaces of Toeplitz operators
Azoff, EA
Ptak, M
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 156 (02) : 411 - 428
[4] Hyper-reflexivity and the factorization of linear functionals
Bercovici, H
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 158 (01) : 242 - 252
[5] BERCOVICI H, 1985, CBMS REGIONAL C SERI, V56
[6] Bercovici H., 1988, Mathematical Surveys and Monographs, V26
[7] BINDNER D, 2001, THESIS U GEORGIA
[8] Conway J. B., 2000, COURSE OPERATOR THEO
[9] DIRECT SUM OF NORMAL OPERATORS
CONWAY, JB
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1977, 26 (02) : 277 - 289
[10] REFLEXIVE LINEAR TRANSFORMATIONS
DEDDENS, JA
FILLMORE, PA
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1975, 10 (01) : 89 - 93

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