Podal subspaces on the unit polydisk

• Autorzy: Kunyu Guo
• Języki publikacji: EN

Abstrakty

EN

Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(D). To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points. By the methods developed in this note, we can assess when a unitary (resp. similarity) orbit contains a podal (resp. an s-podal) point, and hence provide examples of orbits without such points.

Kategorie tematyczne

• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)
• 47B38: Operators on function spaces (general)
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 2
• Strony: 109-120

Daty

wydano

2002

Twórcy

autor

Kunyu Guo

• Department of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China

Identyfikatory

DOI

10.4064/sm149-2-2