The notion of slant Toeplitz operators Bφ and kth-order slant Toeplitz operators B φ on the Fock ... more 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.
As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz... more As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz operators Bφ is introduced and studied. Necessary and sufficient conditions under which H-Toeplitz operators become co-isometry and partial isometry are obtained. Some of the invariant subspaces and kernels of H-Toeplitz operators are studied. We have obtained the conditions for the compactness and Fredholmness for H-Toeplitz operators. In particular, it has been shown that a non-zero HToeplitz operator can not be a Fredholm operator on the Bergman space. Moreover, we have also discussed the necessary and sufficient conditions for commutativity of H-Toeplitz operators.
The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its c... more The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. We have shown that an operator on the space $H^2$ is slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.
In this article, the necessary conditions for the hyponormality of Toeplitz operator T φ with har... more In this article, the necessary conditions for the hyponormality of Toeplitz operator T φ with harmonic polynomial symbols φ on the Fock space are explored.
In this article we have introduced the notion of Toeplitz composition operators as an extension o... more In this article we have introduced the notion of Toeplitz composition operators as an extension of weighted composition operators on the Fock space F 2 and studied its properties. In particular, we have obtained the conditions for boundedness and compactness of Toeplitz composition operators.
The notion of slant Toeplitz operators Bφ and kth-order slant Toeplitz operators B φ on the Fock ... more 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.
As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz... more As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz operators Bφ is introduced and studied. Necessary and sufficient conditions under which H-Toeplitz operators become co-isometry and partial isometry are obtained. Some of the invariant subspaces and kernels of H-Toeplitz operators are studied. We have obtained the conditions for the compactness and Fredholmness for H-Toeplitz operators. In particular, it has been shown that a non-zero HToeplitz operator can not be a Fredholm operator on the Bergman space. Moreover, we have also discussed the necessary and sufficient conditions for commutativity of H-Toeplitz operators.
The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its c... more The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. We have shown that an operator on the space $H^2$ is slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.
In this article, the necessary conditions for the hyponormality of Toeplitz operator T φ with har... more In this article, the necessary conditions for the hyponormality of Toeplitz operator T φ with harmonic polynomial symbols φ on the Fock space are explored.
In this article we have introduced the notion of Toeplitz composition operators as an extension o... more In this article we have introduced the notion of Toeplitz composition operators as an extension of weighted composition operators on the Fock space F 2 and studied its properties. In particular, we have obtained the conditions for boundedness and compactness of Toeplitz composition operators.
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Papers by SHIVAM SINGH