Cowen-Douglas Operators and Shift Operators

Luo, Jiawei1; Li, Juexian2; Cao, Yang3; Tian, Geng1

2022-10-01

10.1007/s00009-022-02091-6

Mediterranean Journal of Mathematics   影响因子和分区

1660-5446

1660-5454

In this paper, we attempt to understand Cowen-Douglas operators by the way of basis theory and shift operator. For a Cowen-Douglas operator T is an element of B-n(Omega) and a complex number z(0) is an element of Omega, we show that there is a generalized basis {g(k)}(k=0)(infinity), such that the adjoint operator (T - z(0))* is the forward shift on {g(k)}(k=0)(infinity), and if n >= 2, then T - z(0) never is a backward shift on any Markushevich basis. Moreover, we give a characterization of a Cowen-Douglas operator in B-1(Omega) being a backward shift on some Markushevich basis. Also, we show that a multiplication operator defined on Bergman space with a Mobius transformation as its multiplier is a forward shift on some Markushevich basis.

Cowen-Douglas operator shift operator basis theory

SCI

英语

通讯

National Natural Science Foundation of China["11371182","11401283","11271150"]

Mathematics

Mathematics, Applied ; Mathematics

WOS:000844997200002

SPRINGER BASEL AG

Web of Science

1.Liaoning Univ, Sch Math & Stat, Shenyang 110036, Peoples R China
2.Southern Univ Sci & Technol, Sch Math, Shenzhen 518055, Peoples R China
3.Jilin Univ, Sch Math, Changchun 130012, Peoples R China

Luo, Jiawei,Li, Juexian,Cao, Yang,et al. Cowen-Douglas Operators and Shift Operators[J]. Mediterranean Journal of Mathematics,2022,19(5).

Luo, Jiawei,Li, Juexian,Cao, Yang,&Tian, Geng.(2022).Cowen-Douglas Operators and Shift Operators.Mediterranean Journal of Mathematics,19(5).

Luo, Jiawei,et al."Cowen-Douglas Operators and Shift Operators".Mediterranean Journal of Mathematics 19.5(2022).