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Numerical Ranges of Composition Operators by Valentin Matache is a Mathematics article available to read on EtoBox.
What is Numerical Ranges of Composition Operators about?
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 symbol fixes 0 and has infinity norm less than 1 have closed numerical ranges in the shape of a cone-like figure, i.e., a closed convex region with a corner at 1, 0 in its interior, and no other corners. Compact composition operators induced by a univalent symbol whose fixed point is not 0 have numerical ranges without corners, except possibly a corner at 0.
Who reads Numerical Ranges of Composition Operators?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Valentin Matache
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0024-3795)
- Published
- 2001
- Language
- EN
- Field
- Mathematics (Physical Sciences)