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Boundedness of Higher order Hankel Forms, Factorization in Potential Spaces and Derivations
Author(s) -
Cohn William,
Ferguson Sarah H.,
Rochberg Richard
Publication year - 2001
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012727
Subject(s) - mathematics , bounded function , order (exchange) , factorization , multilinear map , hardy space , pure mathematics , cohomology , space (punctuation) , product (mathematics) , algebra over a field , mathematical analysis , geometry , algorithm , linguistics , philosophy , finance , economics
We prove a bounded decomposition for higher order Hankel forms and characterize the first order Hochschild cohomology groups of the disk algebra with coefficients in the space of bounded Hankel forms of some fixed order. Although these groups are non‐trivial, we prove that every bounded derivation is inner and necessarily implemented by a Hankel form of order one higher. In terms of operators, this result extends the similarity result of Aleksandrov and Peller. Both of the main structural theorems here rely on estimates involving multilinear maps on the n ‐fold product of the disk algebra and we obtain several higher order analogues of the factorization results due to Aleksandrov and Peller. 2000 Mathematics Subject Classification : 47B35, 46E15, 46E25.