BEHAVIOR OF HOLOMORPHIC MAPPINGS ON p-COMPACT SETS IN A BANACH SPACE

被引：7

作者：

Aron, Richard M. ^{[1
]}

Caliskan, Erhan ^{[2
]}

Garcia, Domingo ^{[3
]}

Maestre, Manuel ^{[3
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Yildiz Tech Univ, Fac Sci & Arts, Dept Math, TR-34210 Istanbul, Turkey

[3] Univ Valencia, Dept Anal Matemat, Doctor Moliner 50, Burjassot 46100, Valencia, Spain

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 07期

关键词：

Banach spaces; p-compact sets; homogeneous polynomials; holomorphic mappings; HOMOGENEOUS POLYNOMIALS; APPROXIMATION PROPERTY; OPERATORS; SUBSPACES; ADJOINTS; L(P);

D O I：

10.1090/tran/6499

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the behavior of holomorphic mappings on p-compact sets in Banach spaces. We show that the image of a p-compact set by an entire mapping is a p-compact set. Some results related to the localization of p-compact sets in the predual of homogeneous polynomials are also obtained. Finally, the "size" of p-compactness of the image of the unit ball by p-compact linear operators is studied.

引用

页码：4855 / 4871

页数：17

共 50 条

[1] p-Compact holomorphic mappings
Aron, Richard M.
Maestre, Manuel
Rueda, Pilar
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2010, 104 (02) : 353 - 364
[2] On holomorphic mappings with relatively p-compact range
Jimenez-Vargas, A.
[J]. FILOMAT, 2023, 37 (24) : 8067 - 8077
[3] p-Compact holomorphic mappings; [Aplicaciones holomorfas p-compactas]
Aron R.M.
Maestre M.
Rueda P.
[J]. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2010, 104 (2) : 353 - 364
[4] Lipschitz p-compact mappings
Achour, Dahmane
Dahia, Elhadj
Turco, Pablo
[J]. MONATSHEFTE FUR MATHEMATIK, 2019, 189 (04): : 595 - 609
[5] Lipschitz p-compact mappings
Dahmane Achour
Elhadj Dahia
Pablo Turco
[J]. Monatshefte für Mathematik, 2019, 189 : 595 - 609
[6] Operator p-compact mappings
Chavez-Dominguez, Javier Alejandro
Dimant, Veronica
Galicer, Daniel
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 277 (08) : 2865 - 2891
[7] Compact sets of holomorphic mappings
Boyd, C
Dineen, S
[J]. MATHEMATISCHE NACHRICHTEN, 1998, 193 : 27 - 36
[8] FURTHER REMARKS ON NONLINEAR P-COMPACT OPERATORS IN BANACH SPACE
PETRYSHY.WV
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1966, 55 (04) : 684 - &
[9] FURTHER REMARKS ON NONLINEAR P-COMPACT OPERATORS IN BANACH SPACE
PETRYSHYN, WV
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1966, 16 (02) : 243 - +
[10] Uniform factorization for p-compact sets of p-compact linear operators
Caliskan, Erhan
Keten, Aysegul
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 437 (02) : 1058 - 1069

← 1 2 3 4 5 →