Release Time:2020-08-13  Hits:

Indexed by: Journal Papers

Date of Publication: 2020-07-24

Journal: COMPLEX ANALYSIS AND OPERATOR THEORY

Included Journals: SCIE

Volume: 14

Issue: 6

ISSN: 1661-8254

Key Words: Reducibility; Truncated Toeplitz operator; Model space

Abstract: Let T be a contraction on the Hilbert space H and S a minimal isometric dilation of T. In this paper, we show that every projection in {T}' can be extended to a projection in {S}'. Using this result, a sufficient condition for reducibility of A(Bn)theta, where B-n is a finite Blaschke product with order n, is given. In particular, we determine when A(Bn)(theta) is reducible in two special cases. One case is that n = 2, 3 and the other case is that B-n = z(n) (n is an element of N) and theta is a singular inner function.