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Full-Text Articles in Physical Sciences and Mathematics
Isometric Weighted Composition Operators, Valentin Matache
Isometric Weighted Composition Operators, Valentin Matache
Mathematics Faculty Publications
A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We find their Wold decomposition in select cases and apply it to the computation of numerical ranges.
Numerical Ranges Of Composition Operators With Inner Symbols, Valentin Matache
Numerical Ranges Of Composition Operators With Inner Symbols, Valentin Matache
Mathematics Faculty Publications
Operators on function paces acting by composition to the right with a fixed self-map φ of some set are called composition operators with the symbol φ. In this paper, composition operators on the Hilbert Hardy space over the unit disk are considered. The numerical ranges of composition operators with inner symbol of parabolic automorphic type of hyperbolic type are shown to be circular.
When Is The Numerical Range Of A Nilpotent Matrix Circular?, Valentin Matache, Mihaela Teodora Matache
When Is The Numerical Range Of A Nilpotent Matrix Circular?, Valentin Matache, Mihaela Teodora Matache
Mathematics Faculty Publications
The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces tr M∗M2 and tr M∗M3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5×5nilpotent matrix has circular numerical range are thoroughly discussed.
Numerical Ranges Of Composition Operators, Valentin Matache
Numerical Ranges Of Composition Operators, Valentin Matache
Mathematics Faculty Publications
Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 is a fixed point of the symbol. If 0 is not a fixed point of the symbol 1 is shown to be interior to the numerical range. Some composition operators whose …