TY - JOUR
T1 - Solid bases and functorial constructions for (p-)Banach spaces of analytic functions
AU - Cheng, Guozheng
AU - Fang, Xiang
AU - Liu, Chao
AU - Lu, Yufeng
N1 - Publisher Copyright:
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
PY - 2024/11/1
Y1 - 2024/11/1
N2 - Motivated by new examples of functional Banach spaces over the unit disk, arising as the symbol spaces in the study of random analytic functions, for which the monomials exhibit features of an unconditional basis yet they often don't even form a Schauder basis, we introduce a notion called solid basis for Banach spaces and p-Banach spaces and study its properties. Besides justifying the rich existence of solid bases, we study their relationship with unconditional bases, the weak-star convergence of Taylor polynomials, the problem of a solid span and the curious roles played by c0. The two features of this work are as follows: (1) during the process, we are led to revisit the axioms satisfied by a typical Banach space of analytic functions over the unit disk, leading to a notion of (and), as well as a number of related functorial constructions, which are of independent interests; (2) the main interests of solid basis lie in the case of non-separable (p-)Banach spaces, such as BMOA and the Bloch space instead of VMOA and the little Bloch space.
AB - Motivated by new examples of functional Banach spaces over the unit disk, arising as the symbol spaces in the study of random analytic functions, for which the monomials exhibit features of an unconditional basis yet they often don't even form a Schauder basis, we introduce a notion called solid basis for Banach spaces and p-Banach spaces and study its properties. Besides justifying the rich existence of solid bases, we study their relationship with unconditional bases, the weak-star convergence of Taylor polynomials, the problem of a solid span and the curious roles played by c0. The two features of this work are as follows: (1) during the process, we are led to revisit the axioms satisfied by a typical Banach space of analytic functions over the unit disk, leading to a notion of (and), as well as a number of related functorial constructions, which are of independent interests; (2) the main interests of solid basis lie in the case of non-separable (p-)Banach spaces, such as BMOA and the Bloch space instead of VMOA and the little Bloch space.
KW - Bloch spaces
KW - BMOA
KW - norm convergence of Taylor polynomials
KW - random analytic functions
KW - solid spaces
KW - unconditional bases
UR - http://www.scopus.com/inward/record.url?scp=85204346420&partnerID=8YFLogxK
U2 - 10.1017/S001309152400035X
DO - 10.1017/S001309152400035X
M3 - Article
AN - SCOPUS:85204346420
SN - 0013-0915
VL - 67
SP - 1013
EP - 1044
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
IS - 4
ER -