Product and Commutativity of kth-Order Slant Toeplitz Operators

The commutativity of kth-order slant Toeplitz operators with harmonic polynomial symbols, analytic symbols, and coanalytic symbols is discussed. We show that, on the Lebesgue space and Bergman space, necessary and sufficient conditions for the commutativity of kth-order slant Toeplitz operators are...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013, p.393-403-549
Main Authors: Liu, Chaomei, Lu, Yufeng
Format: Article
Language:English
Subjects:
Commutative law (Mathematics)
Mathematical research
Polynomials
Topological spaces
Online Access:Get full text
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Summary:The commutativity of kth-order slant Toeplitz operators with harmonic polynomial symbols, analytic symbols, and coanalytic symbols is discussed. We show that, on the Lebesgue space and Bergman space, necessary and sufficient conditions for the commutativity of kth-order slant Toeplitz operators are that their symbol functions are linearly dependent. Also, we study the product of two kth-order slant Toeplitz operators and give some necessary and sufficient conditions.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/473916