一类加权Bergman位移的(n,1)-膨胀

证明{Tz1,Tz2,…,Tzn,1,H2(Tn)}是加权Bergman位移{(k+1/n+k)^(1/2)}∞k=1的极小(n,1)-膨胀。

Bergman位移与超等距膨胀

证明了每一个算子是超等距可膨胀的充要条件是T≌P_Hs(sum from l=1 to f(?)M_l)|H,而H∈Lat(sum from l=1 to q(?)M_l),M_l是Bergman位移,l≤q≤∞。

SUPER-ISOMETRICALLY DILATABLE OPERATORS

<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, in addition, that for φ,ψ and f in H~∞(D), is unitarily equivalent to M_f iff φ=ψ=f=const. provided some finite condition is satisfied.

算子超等距膨胀的条件

本文在文[1],[2]的基础上,进一步讨论了算子超等距膨胀的性质,证明了T∈L(H)可超等距膨胀的充分必要条件是T≌P_H M|_H,或者T≌∑■ P_H M|_H这里M是Bergman位移,H∈LatM~*。