Open AccessOn Banach ideals satisfying $c_0(\mathcal{A}(X,Y))=\mathcal{A}(X,c_0(Y))$
Author(s) -
Juan Manuel Delgado Sánchez,
Cándido Piñeiro Gómez
Publication year - 2008
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-15073
Subject(s) - mathematics , injective function , ideal (ethics) , banach space , norm (philosophy) , compact operator , discrete mathematics , operator (biology) , pure mathematics , combinatorics , extension (predicate logic) , philosophy , biochemistry , chemistry , epistemology , repressor , political science , computer science , transcription factor , law , gene , programming language
We characterize Banach ideals $[\mathcal{A},a]$ satisfying the equality $c_0(\mathcal{A}(X,Y))= \mathcal{A}(X,c_0(Y))$ for all Banach spaces $X$ and $Y$. Among other results we have proved that $\mathcal{K}$ (the normed operator ideal of all compact operators with the operator norm) is the only injective Banach ideal satisfying the equality.