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Holomorphic functions with large cluster sets
Author(s) -
Alves Thiago R.,
Carando Daniel
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900238
Subject(s) - mathematics , holomorphic function , unit sphere , pure mathematics , ball (mathematics) , dual polyhedron , banach space , separable space , bounded function , mathematical analysis
We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed unit ball of the bidual in the infinite dimensional case). We show that this set is strongly c ‐algebrable for all separable Banach spaces. For specific spaces including ℓpor duals of Lorentz sequence spaces, we have strongly c ‐algebrability and spaceability even for the subalgebra of uniformly continous holomorphic functions on the ball.