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BOUNDEDNESS OF HIGHER ORDER HANKEL FORMS, FACTORIZATION IN POTENTIAL SPACES AND DERIVATIONS

Published online by Cambridge University Press:  16 January 2001

WILLIAM COHN ,
SARAH H. FERGUSON  and
RICHARD ROCHBERG
WILLIAM COHN
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, USA, cohn@math.wayne.edu
SARAH H. FERGUSON
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, USA, sarah@math.wayne.edu
RICHARD ROCHBERG
Affiliation:
Department of Mathematics, Campus Box 1146, Washington University, St Louis, MO 63130, USA, rr@math.wustl.edu
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Abstract

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.

Keywords

higher order Hankel formsweak factorizationderivations
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 82 , Issue 1 , January 2001 , pp. 110 - 130
Copyright
2001 London Mathematical Society

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