In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant subspaces of the Segal-Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.
✦ LIBER ✦
Invariant subspaces and localizable spectrum
✍ Scribed by Jörg Eschmeier; Bebe Prunaru
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2002
- Tongue
- English
- Weight
- 464 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0378-620X
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Let X be a complex infinite dimensional Banach space. An operator L on X is called of subcritical class, if n=1 n &3Â2 log + &L n &< . Assume that T is an operator on X whose iterates have norms of polynomial growth. We prove that if T has a range of finite codimension and a left inverse of subcriti