Finite rank intermediate Hankel operators

1996 ◽  
Vol 67 (2) ◽  
pp. 142-149 ◽  
Author(s):  
Elizabeth Strouse
Keyword(s):  
Finite Rank ◽  
Hankel Operators

scholarly journals Finite-rank intermediate Hankel operators on the Bergman space

2001 ◽  
Vol 25 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Takahiko Nakazi ◽  
Tomoko Osawa
Keyword(s):  
Bergman Space ◽  
Orthogonal Projection ◽  
Finite Rank ◽  
Lebesgue Space ◽  
Unit Disc ◽  
Hankel Operator ◽  
Hankel Operators ◽  
Weighted Bergman Space ◽  
Open Unit ◽  
Open Unit Disc

LetL2=L2(D,r dr dθ/π)be the Lebesgue space on the open unit disc and letLa2=L2∩ℋol(D)be the Bergman space. LetPbe the orthogonal projection ofL2ontoLa2and letQbe the orthogonal projection ontoL¯a,02={g∈L2;g¯∈La2,   g(0)=0}. ThenI−P≥Q. The big Hankel operator and the small Hankel operator onLa2are defined as: forϕinL∞,Hϕbig(f)=(I−P)(ϕf)andHϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediate Hankel operators betweenHϕbigandHϕsmallare studied. We are working on the more general space, that is, the weighted Bergman space.

scholarly journals On finite rank Hankel operators

2015 ◽  
Vol 268 (7) ◽  
pp. 1808-1839 ◽  
Author(s):  
D.R. Yafaev
Keyword(s):  
Finite Rank ◽  
Hankel Operators

scholarly journals Zero, finite rank, and compact big truncated Hankel operators on model spaces

2018 ◽  
Vol 146 (12) ◽  
pp. 5235-5242 ◽  
Author(s):  
Pan Ma ◽  
Fugang Yan ◽  
Dechao Zheng
Keyword(s):  
Finite Rank ◽  
Hankel Operators ◽  
Model Spaces

scholarly journals Finite rank intermediate Hankel operators and the big Hankel operator

2006 ◽  
Vol 2006 ◽  
pp. 1-3 ◽  
Author(s):  
Tomoko Osawa
Keyword(s):  
Bergman Space ◽  
Finite Rank ◽  
Hankel Operator ◽  
Closed Subspace ◽  
Hankel Operators ◽  
Coordinate Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

LetLa2be a Bergman space. We are interested in an intermediate Hankel operatorHφMfromLa2to a closed subspaceMofL2which is invariant under the multiplication by the coordinate functionz. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in caseHφMis close to big Hankel operator. As a result, we give a necessary and sufficient condition aboutMthat there does not exist a finite rankHφMexceptHφM=0.

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