Compressions of kth-order slant Toeplitz operators to model spaces

Product and Commutativity of kth-Order Slant Toeplitz Operators

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...

kTH-ORDER SLANT TOEPLITZ OPERATORS ON THE FOCK SPACE

The notion of slant Toeplitz operators Bφ and kth-order slant Toeplitz operators B φ on the Fock space is introduced and some of its properties are investigated. The Berezin transform of slant Toeplitz operator Bφ is also obtained. In addition, the commutativity of kth-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.

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...

Essentially Slant Toeplitz Operators

The notion of an essentially slant Toeplitz operator on the space L is introduced and some of the properties of the set ESTO(L), the set of all essentially slant Toeplitz operators on L, are investigated. In particular the conditions under which the product of two operators in ESTO(L) is in ESTO(L) are discussed. The notion is generalized to kth-order essentially slant Toeplitz operators. The n...

Toeplitz Operators on Fock Spaces