Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900266 | Journal of Mathematical Analysis and Applications | 2018 | 14 Pages |
Abstract
Let S be a pure bounded rationally multicyclic subnormal operator on a separable complex Hilbert space H and let Mz be the minimal normal extension on a separable complex Hilbert space K containing H. Let bpe(S) be the set of bounded point evaluations and let abpe(S) be the set of analytic bounded point evaluations. We show abpe(S)=bpe(S)â©Int(Ï(S)). The result affirmatively answers a question asked by J. B. Conway concerning the equality of the interior of bpe(S) and abpe(S) for a rationally multicyclic subnormal operator S. As a result, if λ0âInt(Ï(S)) and dim(ker(Sâλ0)â)=N, where N is the minimal number of cyclic vectors for S, then the range of Sâλ0 is closed, hence, λ0âÏ(S)âÏe(S).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Liming Yang,