This is a book about a beautiful subject that begins with the topic of Möbius transformations.
Indeed, Möbius transformations z↦→ az+ b cz+ d are studied in complex analysis since their …

For a contraction P and a bounded commutant S of P, we seek a solution X of the operator
equation where X is a bounded operator on [Formula: see text] with numerical radius of X …

Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version,
quantum singular value transformation (QSVT), unify and improve the presentation of most …

This textbook originates from a course for graduate students that I taught at Konstanz
University approximately five or six times over the past twenty years. While the first part of the …

Let 0< ρ≤ 2 and w ρ (X) be the operator radius of a bounded linear Hilbert space operator
X. In this paper we present characterizations of operators satisfying w ρ (X)≤ 1. We also …

For every bivariate polynomial p (z_1, z_2) p (z 1, z 2) of bidegree (n_1, n_2)(n 1, n 2), with p
(0, 0)= 1 p (0, 0)= 1, which has no zeros in the open unit bidisk, we construct a determinantal …

The classical Truncated Moment problem asks for necessary and sufficient conditions so
that a linear functional $ L $ on $\mathcal {P} _ {d} $, the vector space of real $ n $-variable …

Haviland's theorem states that given a closed subset K in Rn, each functional L: R [x¯]→ R
positive on Pos (K)≔{p∈ R [x¯]| p| K≥ 0} admits an integral representation by a positive …

We consider operator systems associated to spectral truncations of tori. We show that their
state spaces, when equipped with the Connes distance function, converge in the Gromov …

The pentablock, denoted as P, is defined as follows: P={(a 21, tr (A), det (A)): A=[aij] 2× 2
with‖ A‖< 1}. It originated from the work of Agler–Lykova–Young in connection with a …