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Generalized Hankel operators on the Fock space II
Author(s) -
Schneider Georg,
Schneider Kristan
Publication year - 2011
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.200910149
Subject(s) - holomorphic function , mathematics , combinatorics , space (punctuation) , connection (principal bundle) , projection (relational algebra) , fock space , algebra over a field , mathematical physics , physics , mathematical analysis , geometry , pure mathematics , quantum mechanics , algorithm , philosophy , linguistics
In this paper we study boundedness of generalized Hankel operators of the form \documentclass{article}\usepackage{amssymb,mathrsfs}\begin{document}\pagestyle{empty}${\rm H}_{{\overline{z}}^k}^l: {\mathscr F}^2\big (|z|^2\big )\rightarrow L^2\big (|z|^2\big )$\end{document} and thereby extend our results from 10. Here, \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\rm H_{{\overline{z}}^k}^l(f):=(\rm Id-\rm P_l)\big (\overline{z}^k f\big )$\end{document} and P l is the projection onto \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$A^2_l\big (\mathbb C,| z|^2\big ):=\rm cl\big (\rm span\lbrace \overline{z} ^mz^n\,|\,m,n\in \mathbb N,\,m\le l\rbrace \big )$\end{document} . Additionally, we extend our results to general conjugate‐holomorphic L 2 symbols. The arguments applied show a tight connection between operator theory and combinatorics.