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Indexed by:Journal Papers

Date of Publication:2020-07-24

Journal:COMPLEX ANALYSIS AND OPERATOR THEORY

Included Journals:SCIE

Volume:14

Issue:6

ISSN No.: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.