Abstract. Completing research made in [K2], we characterize vectors of a Hilbert space, which have a canonical, inner--outer-type factorization in relation to a given operator $T$. Special emphasis is put on the case, when $T$ is an operator admitting an $H^{\infty }$-functional calculus, and, in particular, when $T$ is quasisimilar to the unilateral shift.
AMS Subject Classification
(1991): 47A16, 47A45, 47A60, 47B35
Keyword(s):
Paley type inequalities,
multipliers,
Walsh system,
spline functions,
Ciesielski system,
Hardy spaces,
atomic decomposition
Received October 10, 2003. (Registered under 5815/2009.)
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