Commutative Toeplitz Banach Algebras on the Ball and Quasi-Nilpotent Group Action |
| |
Authors: | Wolfram?Bauer Email author" target="_blank">Nikolai?VasilevskiEmail author |
| |
Institution: | 1.Mathematisches Institut,Georg-August-Universit?t,G?ttingen,Germany;2.Departamento de Matemáticas,CINVESTAV del I.P.N.,Mexico,Mexico |
| |
Abstract: | Studying commutative C*-algebras generated by Toeplitz operators on the unit ball it was proved that, given a maximal commutative subgroup of biholomorphisms
of the unit ball, the C*-algebra generated by Toeplitz operators, whose symbols are invariant under the action of this subgroup, is commutative on
each standard weighted Bergman space. There are five different pairwise non-conjugate model classes of such subgroups: quasi-elliptic, quasi-parabolic, quasi-hyperbolic, nilpotent and quasi-nilpotent. Recently it was observed in Vasilevski (Integr Equ Oper Theory. 66:141–152, 2010) that there are many other, not geometrically defined, classes of symbols which generate commutative Toeplitz operator algebras
on each weighted Bergman space. These classes of symbols were subordinated to the quasi-elliptic group, the corresponding commutative operator algebras were Banach, and being extended to C*-algebras they became non-commutative. These results were extended then to the classes of symbols, subordinated to the quasi-hyperbolic and quasi-parabolic groups. In this paper we prove the analogous commutativity result for Toeplitz operators whose symbols are subordinated to
the quasi-nilpotent group. At the same time we conjecture that apart from the known C*-algebra cases there are no more new Banach algebras generated by Toeplitz operators whose symbols are subordinated to the
nilpotent group and which are commutative on each weighted Bergman space. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|