منابع مشابه
Smooth Functions in Star-invariant Subspaces
In this note we summarize some necessary and sufficient conditions for subspaces invariant with respect to the backward shift to contain smooth functions. We also discuss smoothness of moduli of functions in such subspaces.
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The main purpose of this article is to give an approach to the recent invariant subspace theorem of Brown, Chevreau and Pearcy: Every contraction on a Hubert space, whose spectrum contains the unit circle has nontrivial invariant subspaces. Our proof incorporates several of the recent ideas tying together function theory and operator theory. 1. I N T R O D U C T I O N The Jordan structure theor...
متن کاملWeak compactness in certain star-shift invariant subspaces
The context of much of the work in this paper is that of a backward-shift invariant subspace of the form KB :1⁄4 HðDÞ~BHðDÞ; where B is some infinite Blaschke product. We address (but do not fully answer) the question: For which B can one find a (convergent) sequence f fngn1⁄41 in KB such that the sequence of real measures flog j fnjdyg N n1⁄41 converges weak-star to some nontrivial singular me...
متن کاملBad boundary behavior in star invariant subspaces I
We discuss the boundary behavior of functions in star invariant subspaces (BH2)⊥, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.
متن کاملBad Boundary Behavior in Star Invariant Subspaces II
We continue our study begun in [HR11] concerning the radial growth of functions in the model spaces (IH).
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12465-x