scholarly journals Interpolation by multipliers on certain spaces of analytic functions

2000 ◽  
Vol 23 (8) ◽  
pp. 547-554
Author(s):  
K. Mosaleheh ◽  
K. Seddighi
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Linear Functional ◽  
Dirichlet Space ◽  
Planar Domain ◽  
Space Of Analytic Functions ◽  
Spectral Set ◽  
Spaces Of Analytic Functions

Letℋbe a Hilbert space of analytic functions on a planar domainGsuch that, for eachλinG, the linear functionaleλof evaluation atλis bounded onℋ. Furthermore, assume thatzℋ⊂ℋandσ(Mz)=G¯is anM-spectral set forMz, the operator of multiplication byz. This paper is devoted to the study of interpolation by multipliers of the spaceℋand, in particular, the Dirichlet space.

scholarly journals On Some Properties of Cowen-Douglas Class of Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Parastoo Heiatian Naeini ◽  
Bahmann Yousefi
Keyword(s):  
Hilbert Space ◽  
Analytic Function ◽  
Essential Spectrum ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Space Of Analytic Functions ◽  
Class Operator ◽  
Necessary And Sufficient

We will consider multiplication operators on a Hilbert space of analytic functions on a domainΩ⊂C. For a bounded analytic functionφonΩ, we will give necessary and sufficient conditions under which the complement of the essential spectrum ofMφinφΩbecomes nonempty and this gives conditions for the adjoint of the multiplication operatorMφbelongs to the Cowen-Douglas class of operators. Also, we characterize the structure of the essential spectrum of a multiplication operator and we determine the commutants of certain multiplication operators. Finally, we investigate the reflexivity of a Cowen-Douglas class operator.

Compact differences of composition operators on weighted Dirichlet spaces

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Robert Allen ◽  
Katherine Heller ◽  
Matthew Pons
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Complex Interpolation ◽  
Dirichlet Spaces ◽  
Space Of Analytic Functions ◽  
First Derivative ◽  
Weighted Dirichlet Spaces ◽  
The Difference

AbstractHere we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

Hausdorff and Quasi-Hausdorff Matrices on Spaces of Analytic Functions

2006 ◽  
Vol 58 (3) ◽  
pp. 548-579 ◽  
Author(s):  
P. Galanopoulos ◽  
M. Papadimitrakis
Keyword(s):  
Analytic Functions ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Moment Sequence ◽  
Bloch Spaces ◽  
The Matrix ◽  
Generating Sequence ◽  
Hausdorff Matrices ◽  
The Moment ◽  
Spaces Of Analytic Functions

AbstractWe consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and BMOA. When the generating sequence of the matrix is the moment sequence of a measure μ, we find the conditions on μ which are equivalent to the boundedness of the matrix on the various spaces.

scholarly journals Multipliers on Spaces of Analytic Functions

1995 ◽  
Vol 47 (1) ◽  
pp. 44-64 ◽  
Author(s):  
Oscar Blasco
Keyword(s):  
Hardy Spaces ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Space Of Analytic Functions ◽  
Spaces Of Analytic Functions

AbstractIn the paper we find, for certain values of the parameters, the spaces of multipliers (H(p, q, α), H(s, t, β) and (H(p, q, α), ls), where H(p, q, α) denotes the space of analytic functions on the unit disc such that . As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces.

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