Operators having the symmetrized bidisc as a spectral set
نویسندگان
چکیده
منابع مشابه
From Stinespring dilation to Sz.-Nagy dilation on the symmetrized bidisc and operator models
We provide an explicit normal distinguished boundary dilation to a pair of commuting operators (S, P ) having the closed symmetrized bidisc Γ as a spectral set. This is called Sz.-Nagy dilation of (S, P ). The operator pair that dilates (S, P ) is obtained by an application of Stinespring dilation of (S, P ) given by Agler and Young. We further prove that the dilation is minimal and the dilatio...
متن کاملThe Semi-commutator of Toeplitz Operators on the Bidisc
In this paper we characterize when the semi-commutator TfTg − Tfg of two Toeplitz operators Tf and Tg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T 2 are given.
متن کاملSymmetrized Trace and Symmetrized Determinant of Odd Class Pseudo-differential Operators
We introduce a new canonical trace on odd class logarithmic pseudo-differential operators on an odd dimensional manifold, which vanishes on a commutators. When restricted to the algebra of odd class classical pseudo-differential operators our trace coincides with the canonical trace of Kontsevich and Vishik. Using the new trace we construct a new determinant of odd class classical elliptic pseu...
متن کاملDynamics in the Complex Bidisc
Let ∆n be the unit polydisc in Cn and let f be a holomorphic self map of ∆n. When n = 1, it is well known, by Schwarz’s lemma, that f has at most one fixed point in the unit disc. If no such point exists then f has a unique boundary point, call it x ∈ ∂∆, such that every horocycle E(x, R) of center x and radius R > 0 is sent into itself by f . This boundary point is called the Wolff point of f....
متن کاملHill Operators and Spectral Operators of Scalar
We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H = −d 2 /dx 2 + V in L 2 (R) to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. R ´ ESUMÉ. Quand un op...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2000
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500020812