scholarly journals Multiplication operators on weighted Bloch spaces of the first Cartan domains

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhi-jie Jiang
Keyword(s):  
Multiplication Operators ◽  
Bloch Spaces

Boundedness From Below of Multiplication Operators Between α-Bloch Spaces

2010 ◽  
Vol 53 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Huaihui Chen ◽  
Minzhu Zhang
Keyword(s):  
Unit Disk ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Bloch Spaces ◽  
Bounded Below

AbstractIn this paper, the boundedness from below of multiplication operators between α-Bloch spaces , α > 0, on the unit disk D is studied completely. For a bounded multiplication operator , defined by Muƒ = u ƒ for f ∈ , we prove the following result:(i) If 0 < β < α, or 0 < α ≤ 1 and α < β, Mu is not bounded below;(ii) if 0 < α = β ≤ 1, Mu is bounded below if and only if lim infz→∂D |u(z)| > 0;(iii) if 1 < α ≤ β,Mu is bounded below if and only if there exist a δ > 0 and a positive r < 1 such that for every point z ∈ D there is a point z′ ∈ D with the property d(z′, z) < r and (1–|z′|2)β–α|u(z′)| ≥ δ, where d( · , · ) denotes the pseudo-distance on D.

Riemann-Stieltjes operators between α -Bloch spaces and Besov spaces

2009 ◽  
Vol 282 (6) ◽  
pp. 899-911 ◽  
Author(s):  
Songxiao Li ◽  
Stevo Stević
Keyword(s):  
Besov Spaces ◽  
Bloch Spaces

DIAGONALIZATION MODULO NORM IDEALS AND HAUSDORFF DIMENSIONALITY

2000 ◽  
Vol 11 (08) ◽  
pp. 1057-1078
Author(s):  
JINGBO XIA
Keyword(s):  
Hausdorff Measure ◽  
Metric Spaces ◽  
Adjoint Operator ◽  
Trace Class ◽  
Multiplication Operators ◽  
Von Neumann ◽  
Dimensional Hausdorff Measure ◽  
One Dimensional ◽  
Compact Metric Spaces ◽  
The One

Kuroda's version of the Weyl-von Neumann theorem asserts that, given any norm ideal [Formula: see text] not contained in the trace class [Formula: see text], every self-adjoint operator A admits the decomposition A=D+K, where D is a self-adjoint diagonal operator and [Formula: see text]. We extend this theorem to the setting of multiplication operators on compact metric spaces (X, d). We show that if μ is a regular Borel measure on X which has a σ-finite one-dimensional Hausdorff measure, then the family {Mf:f∈ Lip (X)} of multiplication operators on T2(X, μ) can be simultaneously diagonalized modulo any [Formula: see text]. Because the condition [Formula: see text] in general cannot be dropped (Kato-Rosenblum theorem), this establishes a special relation between [Formula: see text] and the one-dimensional Hausdorff measure. The main result of the paper is that such a relation breaks down in Hausdorff dimensions p>1.

scholarly journals Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces toHμ∞

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Shanli Ye
Keyword(s):  
Lower Bound ◽  
Unit Disk ◽  
Weighted Space ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces

In this note we express the norm of composition followed by differentiationDCφfrom the logarithmic Bloch and the little logarithmic Bloch spaces to the weighted spaceHμ∞on the unit disk and give an upper and a lower bound for the essential norm of this operator from the logarithmic Bloch space toHμ∞.

Sign in / Sign up

Export Citation Format

Share Document