ALGEBRAIC REFLEXIVITY OF SETS OF BOUNDED LINEAR OPERATORS ON ABSOLUTELY CONTINUOUS FUNCTION SPACES

被引：10

作者：

Hosseini, Maliheh ^{[1
]}

机构：

[1] KN Toosi Univ Technol, Fac Math, Tehran 163151618, Iran

来源：

OPERATORS AND MATRICES | 2019年 / 13卷 / 03期

关键词：

Algebraic reflexivity; isometry group; absolutely continuous function; generalized bi-circular projection; isometric reflection; BI-CIRCULAR PROJECTIONS; LOCAL ISOMETRIES;

D O I：

10.7153/oam-2019-13-63

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we deal with the algebraic reflexivity of sets of bounded linear operators on absolutely continuous vector-valued function spaces. As a consequence, it is shown that the set of all surjective linear isometries, the set of all isometric reflections, and the set of all generalized bi-circular projections on AC[0,1] are algebraically reflexive.

引用

页码：887 / 895

页数：9

共 12 条

[1] Reflexivity of sets of isometries on bounded variation function spaces
Hosseini, Maliheh
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (19) : 4405 - 4415
[2] Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions
Botelho, Fernanda
Jamison, James
LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (12) : 3337 - 3342
[3] On algebraic reflexivity of sets of surjective isometries between spaces of weak* continuous functions
Botelho, Fernanda
Rao, T. S. S. R. K.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 432 (01) : 367 - 373
[4] Reflexivity defect of spaces of linear operators
Bracic, Janko
Kuzma, Bojan
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (01) : 344 - 359
[5] Linear isometries on spaces consisting of absolutely continuous functions
Koshimizu H.
Acta Scientiarum Mathematicarum, 2014, 80 (3-4): : 581 - 590
[6] Projections in the Convex Hull of Three Isometries on Absolutely Continuous Function Spaces
Maliheh Hosseini
A. Jiménez-Vargas
Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 3489 - 3509
[7] Projections in the Convex Hull of Three Isometries on Absolutely Continuous Function Spaces
Hosseini, Maliheh
Jimenez-Vargas, A.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (05) : 3489 - 3509
[8] Projections in the convex hull of two isometries of absolutely continuous function spaces
Maliheh Hosseini
Positivity, 2021, 25 : 791 - 799
[9] ALGEBRAIC REFLEXIVITY OF DIAMETER-PRESERVING LINEAR BIJECTIONS BETWEEN C(X)-SPACES
Jimenez-Vargas, A.
Sady, Fereshteh
PUBLICACIONS MATEMATIQUES, 2021, 65 (02) : 727 - 746
[10] Projections in the convex hull of two isometries of absolutely continuous function spaces
Hosseini, Maliheh
POSITIVITY, 2021, 25 (03) : 791 - 799

← 1 2 →