Polynomials and holomorphic functions on A-compact sets in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Lassalle, Silvia^1,2  Turco, Pablo³ 

[1] Univ San Andres, Dept Matemat, Vito Dumas 284,B1644BID, Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, IMAS, Buenos Aires, DF, Argentina

[3] UBA, CONICET, IMAS, Fac Cs Exactas & Nat, Pab 1, RA-1428 Buenos Aires, DF, Argentina

关键词: Banach spaces;    A-compact sets;    Homogeneous polynomials;    Holomorphic functions;   

DOI  :  10.1016/j.jmaa.2018.03.070

来源: Elsevier

【 摘 要 】

In this paper we study the behavior of holomorphic mappings on A-compact sets. Motivated by the recent work of Aron, caliskan, Garcia and Maestre (2016), we give several conditions (on the holomorphic mappings and on the lambda-Banach operator ideal A) under which A-compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of (A; B)-compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any (p, r)-compact set under any holomorphic function (defined on any open set of a Banach space) is again (p, r) -compact. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free