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Non nuclear integral operators with continuous kernels
Author(s) -
Frerick Leonhard
Publication year - 2003
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.200310058
Subject(s) - mathematics , kernel (algebra) , operator (biology) , pure mathematics , algebra over a field , discrete mathematics , chemistry , biochemistry , repressor , transcription factor , gene
In this note we give a positive answer to the following question posed by A. Pietsch: Is there for all p, q ∈ (1, ∞) a continuous kernel K such that the associated integral operator T K : L q ([0, 1]) → L p ([0, 1]) fails to be nuclear?