On a weighted Toeplitz operator and its commutant
نویسندگان
چکیده
منابع مشابه
On a weighted Toeplitz operator and its commutant
We study the structure of a class of weighted Toeplitz operators and obtain a description of the commutant of each operator in this class. We make some progress towards proving that the only operator in the commutant which is not a scalar multiple of the identity operator and which commutes with a nonzero compact operator is zero. The proof of the main statement relies on a conjecture which is ...
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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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15 صفحه اولOn Weighted Toeplitz Operators
A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2005
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms.2005.823