scholarly journals Toeplitz Operators and Hankel Operators on the Hardy Space of the Unit Sphere

1997 ◽  
Vol 149 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Dechao Zheng
Keyword(s):  
Hardy Space ◽  
Unit Sphere ◽  
Toeplitz Operators ◽  
Hankel Operators

scholarly journals COMPACT TOEPLITZ OPERATORS WITH CONTINUOUS SYMBOLS

2009 ◽  
Vol 51 (2) ◽  
pp. 257-261 ◽  
Author(s):  
TRIEU LE
Keyword(s):  
Hardy Space ◽  
Unit Ball ◽  
Unit Sphere ◽  
Orthogonal Projection ◽  
Toeplitz Operators ◽  
Borel Measure ◽  
Borel Function ◽  
Closed Unit Ball ◽  
Rotation Invariant ◽  
Regular Borel Measure

AbstractFor any rotation-invariant positive regular Borel measure ν on the closed unit ball $\overline{\mathbb{B}}_n$ whose support contains the unit sphere $\mathbb{S}_n$, let L2a be the closure in L2 = L2($\overline{\mathbb{B}}_n, dν) of all analytic polynomials. For a bounded Borel function f on $\overline{\mathbb{B}}_n$, the Toeplitz operator Tf is defined by Tf(ϕ) = P(fϕ) for ϕ ∈ L2a, where P is the orthogonal projection from L2 onto L2a. We show that if f is continuous on $\overline{\mathbb{B}}_n$, then Tf is compact if and only if f(z) = 0 for all z on the unit sphere. This is well known when L2a is replaced by the classical Bergman or Hardy space.

Singular Integral Operators and Essential Commutativity on the Sphere

2010 ◽  
Vol 62 (4) ◽  
pp. 889-913 ◽  
Author(s):  
Jingbo Xia
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Unit Sphere ◽  
Toeplitz Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Essential Commutant

AbstractLet 𝒯 be the C*-algebra generated by the Toeplitz operators {T𝜑 : 𝜑 Є L∞(S, dσ)} on the Hardy space H2(S) of the unit sphere in Cn. It is well known that 𝒯 is contained in the essential commutant of {T𝜑 : 𝜑 Є VMO∩L∞(S, dσ)}. We show that the essential commutant of {T𝜑 : 𝜑 Є VMO∩L∞(S, dσ)} is strictly larger than 𝒯.

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2

1998 ◽  
Vol 50 (3) ◽  
pp. 658-672 ◽  
Author(s):  
Frédéric Symesak
Keyword(s):  
Hardy Space ◽  
Finite Type ◽  
Pseudoconvex Domain ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Sufficient Condition ◽  
Schatten Class ◽  
Strictly Pseudoconvex Domain

AbstractThe aimof this paper is to study small Hankel operators h on the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2 or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbol ƒ so that h belongs to the Schatten class Sp, 1 ≤ p < +∞.

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