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Approximation by Weakly Compact Operators in L 1
Author(s) -
Weis L.
Publication year - 1984
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.19841190128
Subject(s) - mathematics , compact operator , bounded function , linear operators , approximation property , operator (biology) , ideal (ethics) , element (criminal law) , pure mathematics , operator theory , finite rank operator , bounded operator , compact operator on hilbert space , discrete mathematics , mathematical analysis , banach space , extension (predicate logic) , computer science , biochemistry , chemistry , philosophy , epistemology , repressor , transcription factor , law , political science , gene , programming language
For every bounded linear operator T in L 1 [0, 1] there is an element of best approximation in the ideal of weakly compact operators. We also give some sufficient conditions for ‖ T + S ‖ = ‖T‖ + ‖ S ‖, where S and T are L 1 ‐operators.