Hypercyclicity of weighted composition operators on the weighted little Bloch space

2020 ◽  
Vol 31 (1) ◽  
pp. 106-116
Author(s):  
Hang Zhou ◽  
Ning Zhou ◽  
Shi-An Han ◽  
Ze-Hua Zhou
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Little Bloch Space

scholarly journals Weighted composition operators on the Bloch space

2001 ◽  
Vol 63 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Shûichi Ohno ◽  
Ruhan Zhao
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Pointwise Multipliers ◽  
Weighted Composition ◽  
Little Bloch Space

We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and pointwise multipliers on the Bloch space and the little Bloch space.

scholarly journals SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP

2012 ◽  
Vol 55 (1) ◽  
pp. 229-239 ◽  
Author(s):  
KEI JI IZUCHI ◽  
KOU HEI IZUCHI ◽  
YUKO IZUCHI
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Disk Algebra ◽  
Weighted Composition ◽  
Little Bloch Space

AbstractLet COP =0∩H∞, where0is the little Bloch space on the open unit disk, andA() be the disk algebra on. For non-zero functionsu1,u2,. . .,uN∈A() and distinct analytic self-maps ϕ1,ϕ2,. . .,ϕNsatisfying ϕj∈A() and ∥ϕj∥∞=1 for everyj, it is given characterisations of which the sum of weighted composition operators ∑Nj=1ujCϕjmaps COP intoA().

scholarly journals Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Banach Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Weighted Composition

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk&#x1D53B;whose elementsfsatisfy the condition∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|=0.

scholarly journals ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE

2009 ◽  
Vol 79 (1) ◽  
pp. 147-160 ◽  
Author(s):  
ROBERT F. ALLEN ◽  
FLAVIA COLONNA
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

AbstractIn this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

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