@inbook{1e4f68158a844b4ea0221c2cd4e5358e,
title = "Hermitian Metrics on the Resolvent Set and Extremal Arc Length",
abstract = "For a bounded linear operator A on a complex Hilbert space the functions where defines a family of Hermitian metrics on the resolvent set Thus the arc length of a fixed circle C ⊂ with respect to the metric gx is dependent on the choice of x. This paper derives an integral equation for the extremal values of the arc length. Solution x of the equation, if exists, has particular properties as related to A. In the case A is the unilateral shift operator on the Hardy space H2, the paper proves that the arc length of C is maximal if and only if x is an inner function.",
keywords = "Extremal equation, Hermitian metric, Inner function, Nilpotent operator, Resolvent set, Unilateral shift",
author = "Mai Tran and Rongwei Yang",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",
year = "2020",
doi = "10.1007/978-3-030-43380-2\_23",
language = "English",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "487--499",
booktitle = "Operator Theory",
}