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A Factorization Property of R ‐Bounded Sets of Operators on L p ‐Spaces
Author(s) -
Le Merdy Christian,
Simard Arnaud
Publication year - 2002
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 - 10.1002/1522-2616(200209)243:1<146::aid-mana146>3.0.co;2-o
Subject(s) - mathematics , bounded function , bounded operator , operator (biology) , factorization , space (punctuation) , set (abstract data type) , property (philosophy) , discrete mathematics , operator theory , finite rank operator , pure mathematics , banach space , mathematical analysis , algorithm , computer science , biochemistry , chemistry , philosophy , epistemology , repressor , transcription factor , gene , programming language , operating system
Let T be a bounded operator on L p ‐space, with 1 ≤ p < ∞. A theorem of W. B. Johnson and L. Jones asserts that after an appropriate change of density, T actually extends to a bounded operator on L 2 . We show that if ⊂ B ( L p ) is an R ‐bounded set of operators, then the latter result holds for any T ∈ with a common change of density. Then we give applications including results on R ‐sectorial operators.