On th-Order Slant Weighted Toeplitz Operator
نویسندگان
چکیده
منابع مشابه
On kth-Order Slant Weighted Toeplitz Operator
Let β = [formula: see text] be a sequence of positive numbers with β0 = 1, 0 < β(n)/β(n+1) ≤ 1 when n ≥ 0 and 0 < β(n)/β(n-1) ≤ 1 when n ≤ 0. A kth-order slant weighted Toeplitz operator on L(2)(β) is given by U(φ) = W(k)M(φ), where M(φ) is the multiplication on L(2)(β) and W(k) is an operator on L(2)(β) given by W(k)e(nk)(z) = (β(n)/β(nk))e(n)(z), [formula: see text] being the orthonormal basi...
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A slant weighted Toeplitz operator Aφ is an operator on L(β) defined as Aφ = WMφ where Mφ is the weighted multiplication operator and W is an operator on L(β) given by We2n = βn β2n en, {en}n∈Z being the orthonormal basis. In this paper, we generalise Aφ to the k-th order slant weighted Toeplitz operator Uφ and study its properties. Keywords—Slant weighted Toeplitz operator, weighted multiplica...
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and Applied Analysis 3 Theorem3. Letφ, ψ∈H∞(T) orφ,ψ ∈ H(T), the following statements are equivalent: (1.1) U φ and U ψ commute; (1.2) U φ and U ψ essentially commute; (1.3) φ(zk)ψ(z) = φ(z)ψ(z); (1.4) there exist scalars α andβ, not both zero, such that αφ+ βψ = 0. Nowwe start to study the commutativity of two kth-order slant Toeplitz operators with harmonic symbols. Proposition4. Letφ(z)=∑n p...
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ژورنال
عنوان ژورنال: The Scientific World Journal
سال: 2013
ISSN: 1537-744X
DOI: 10.1155/2013/960853