TY - JOUR

T1 - Canonical operator models over reinhardt domains

AU - Fang, Xiang

PY - 2007/3

Y1 - 2007/3

N2 - Through the works of many, now it is well known that the existence of dilation to the direct sum of a weighted shift is guaranteed by a positivity condition and a convergence condition. But the uniqueness of dilation is still not well understood. In this paper we show that a theory of canonical operator models, not just the existence of dilation, can be achieved for general weighted shifts, with a level of sophistication at least close to that for the d-shifts on the symmetric Fock spaces. Most techniques used in the paper are known, but we do have new ingredients which give a clearer picture even on the symmetric Fock space, where a nice theory has been developed by Arveson.

AB - Through the works of many, now it is well known that the existence of dilation to the direct sum of a weighted shift is guaranteed by a positivity condition and a convergence condition. But the uniqueness of dilation is still not well understood. In this paper we show that a theory of canonical operator models, not just the existence of dilation, can be achieved for general weighted shifts, with a level of sophistication at least close to that for the d-shifts on the symmetric Fock spaces. Most techniques used in the paper are known, but we do have new ingredients which give a clearer picture even on the symmetric Fock space, where a nice theory has been developed by Arveson.

KW - Dilation

KW - Operator models

KW - Reinhardt domain

KW - Weighted shifts

UR - http://www.scopus.com/inward/record.url?scp=34250155587&partnerID=8YFLogxK

U2 - 10.11650/twjm/1500404636

DO - 10.11650/twjm/1500404636

M3 - 期刊論文

AN - SCOPUS:34250155587

SN - 1027-5487

VL - 11

SP - 75

EP - 94

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

IS - 1

ER -