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Podal subspaces on the unit polydisk

100%
Guo K.
Studia Mathematica
|
2002
|
tom 149
|
nr 2
109-120
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.
2
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Normal Hilbert modules over the ball algebra A(B)

100%
Guo K.
Studia Mathematica
|
1999
|
tom 135
|
nr 1
1-12
EN
The normal cohomology functor $Ext_ℵ$ is introduced from the category of all normal Hilbert modules over the ball algebra to the category of A(B)-modules. From the calculation of $Ext_ℵ$-groups, we show that every normal C(∂B)-extension of a normal Hilbert module (viewed as a Hilbert module over A(B) is normal projective and normal injective. It follows that there is a natural isomorphism between Hom of normal Shilov modules and that of their quotient modules, which is a new lifting theorem of normal Shilov modules. Finally, these results are applied to the discussion of rigidity and extensions of Hardy submodules over the ball algebra.
3
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On unitary equivalence of invariant subspaces of the Dirichlet space

64%
Guo K., Zhao L.
Studia Mathematica
|
2010
|
tom 196
|
nr 2
143-150
EN
It is shown that in the Dirichlet space 𝓓, two invariant subspaces ℳ ₁, ℳ ₂ of the Dirichlet shift $M_{z}$ are unitarily equivalent only if ℳ ₁ = ℳ ₂.
4
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Quasi-invariant subspaces generated by polynomials with nonzero leading terms

64%
Guo K., Hou S.
Studia Mathematica
|
2004
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tom 164
|
nr 3
231-241
EN
We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].
5
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Spectral properties of quotients of Beurling-type submodules of the Hardy module over the unit ball

64%
Guo K., Duan Y.
Studia Mathematica
|
2006
|
tom 177
|
nr 2
141-152
EN
Let M be a Beurling-type submodule of $H²(𝔹_{d})$, the Hardy space over the unit ball $𝔹_{d}$ of $ℂ^{d}$, and let $N = H²(𝔹_{d})/M$ be the associated quotient module. We completely describe the spectrum and essential spectrum of N, and related index theory.
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