Free holomorphic functions and interpolation
From MaRDI portal
Publication:938246
DOI10.1007/s00208-008-0219-2zbMath1146.47010arXiv0711.2970OpenAlexW2592814836MaRDI QIDQ938246
Publication date: 18 August 2008
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0711.2970
free holomorphic functions with positive real partsnoncommutative Cayley transformnoncommutative multivariable Nevanlinna-Pick interpolation problemoperator-valued interpolation
Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator methods in interpolation, moment and extension problems (47A57) Noncommutative function spaces (46L52) Holomorphic maps in nonlinear functional analysis (46T25)
Related Items
Operator theory on noncommutative polydomains. I. ⋮ Aspects of non-commutative function theory ⋮ Reflection positivity on real intervals ⋮ Free holomorphic functions on the unit ball of \(B(\mathcal H)^n\). II ⋮ Herglotz functions of several quaternionic variables ⋮ Symmetry in tensor algebras over Hilbert space ⋮ Norm preserving extensions of holomorphic functions defined on varieties in \(\mathbb{C}^n\) ⋮ Non-commutative Carathéodory interpolation ⋮ Analytic mappings between noncommutative pencil balls ⋮ Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem ⋮ Non-commutative holomorphic functions on operator domains ⋮ Non-commutative polynomial solutions to partial differential equations ⋮ Herglotz functions: the Fueter variables case ⋮ Operator-valued Herglotz kernels and functions of positive real part on the ball ⋮ Clark theory in the Drury-Arveson space ⋮ Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation ⋮ Free pluriharmonic majorants and commutant lifting ⋮ Non-commutative functional calculus ⋮ The implicit function theorem and free algebraic sets ⋮ Noncommutative hyperbolic geometry on the unit ball of \(B(\mathcal H)^n\) ⋮ Noncommutative ball maps ⋮ Free holomorphic automorphisms of the unit ball of B(ℋ) n
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hardy algebras, \(W^*\)-correspondences and interpolation theory
- Noncommutative convexity arises from linear matrix inequalities
- Free holomorphic functions on the unit ball of \(B(\mathbb H)^n\)
- The commutant lifting approach to interpolation problems
- On intertwining dilations for sequences of noncommuting operators
- Simple \(C^*\)-algebras generated by isometries
- Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras
- Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
- Interpolation problems in several variables
- Poisson transforms on some \(C^*\)-algebras generated by isometries
- The algebraic structure of non-commutative analytic Toeplitz algebras
- Multivariable Nehari problem and interpolation.
- ``Positive noncommutative polynomials are sums of squares.
- Functional calculus for noncommuting operators
- Multi-analytic operators on Fock spaces
- Noncommutative interpolation and Poisson transforms
- Positivity aspects of the Fantappiè transform
- Noncommutative transforms and free pluriharmonic functions
- The structure of free smigroup algebras
- Spherical contractions and interpolation problems on the unit ball
- Isometric Dilations for Infinite Sequences of Noncommuting Operators
- ON BOHR'S INEQUALITY
- Relations d'un problème de Nevanlinna et Pick avec la théorie des opérateurs de l'espace hilbertien
- Entropy and multivariable interpolation
- Unitary invariants in multivariable operator theory
- Invariant Subspaces and Hyper-Reflexivity for Free Semigroup Algebras
- Von Neumann inequality for $(B(\mathscr{H})^n)_1$.
- Similarity and ergodic theory of positive linear maps
- A non-commutative Positivstellensatz on isometries
- The curvature invariant of a Hilbert module over ℂ [z1, ..., zd]
- A positivstellensatz for non-commutative polynomials
- Non-commutative disc algebras and their representations
- Operator theory on noncommutative varieties
- Generalized Interpolation in H ∞
- Lax-Phillips scattering and conservative linear systems: a Cuntz-algebra multidimensional setting
- Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet
- Positive Functions on C ∗ -Algebras
- Curvature invariant for Hilbert modules over free semigroup algebras
