scholarly journals Ideals and invariant subspaces of analytic functions

1964 ◽  
Vol 111 (3) ◽  
pp. 493-493 ◽  
Author(s):  
Michael Voichick
Keyword(s):  
Analytic Functions ◽  
Invariant Subspaces

Invariant subspaces of given index in Banach spaces of analytic functions

1998 ◽  
Vol 1998 (505) ◽  
pp. 23-44 ◽  
Author(s):  
Alexander Borichev
Keyword(s):  
Banach Spaces ◽  
Wide Class ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Weighted Bergman Spaces ◽  
Common Zeros ◽  
Spaces Of Analytic Functions

Abstract For a wide class of Banach spaces of analytic functions in the unit disc including all weighted Bergman spaces with radial weights and for weighted ℓAp spaces we construct z-invariant subspaces of index n, 2 ≦ n ≦ + ∞, without common zeros in the unit disc.

scholarly journals Invariant subspaces in Banach spaces of analytic functions.

1990 ◽  
Vol 37 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Håkan Hedenmalm ◽  
Allen Shields
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Invariant Subspaces ◽  
Spaces Of Analytic Functions

Invariant Subspace Theorems for Finite Riemann Surfaces

1966 ◽  
Vol 18 ◽  
pp. 240-255 ◽  
Author(s):  
Morisuke Hasumi
Keyword(s):  
Riemann Surface ◽  
Invariant Subspace ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Invariant Subspaces ◽  
Multiply Connected Domains ◽  
Disk Algebra ◽  
Multiply Connected ◽  
Beurling Theorem ◽  
Finite Riemann Surface

The purpose of this paper is to extend various invariant subspace theorems for the circle group to multiply connected domains. Such attempts are not new. Actually, Sarason (4) studied the invariant subspaces of annulus operators acting on L2 and showed certain parallelisms between the unit disk case and the annulus case. Voichick (8) observed analytic functions on a finite Riemann surface and generalized the Beurling theorem on the closed invariant subspaces of H2 as well as the Beurling–Rudin theorem on the closed ideals of the disk algebra. Here we shall consider LP(Γ) and C(Γ) defined on the boundary Γ of a finite orientable Riemann surface R.

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