Equivalence of Boundary Eigenvalue Operator Fuctions and their Characteristic Matrix Functions.
Generalization of Weyl-von Neumann-Berg theorem for the case of normal operator-valued holomorphic functions
Growth of operator valued meromorphic functions.
functional calculus for sectorial and bisectorial operators
We give a concise exposition of the basic theory of functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator when f is an R-bounded operator-valued holomorphic function.
Hermitian Geometry and Involutive Algebras.
Holomorphic Families of Dirac Operators.
Homomorphisms on algebras of Lipschitz functions
We characterize a class of *-homomorphisms on Lip⁎(X,𝓑(𝓗 )), a non-commutative Banach *-algebra of Lipschitz functions on a compact metric space and with values in 𝓑(𝓗 ). We show that the zero map is the only multiplicative *-preserving linear functional on Lip⁎(X,𝓑(𝓗 )). We also establish the algebraic reflexivity property of a class of *-isomorphisms on Lip⁎(X,𝓑(𝓗 )).
Hyperbolic geometry on noncommutative balls.
Inner-outer factorization of operator-valued functions on ordered groups
Inner-outer factorization for matrix-valued functions defined on totally ordered groups has been considered by Helson and Lowdenslager in connection with multivariate prediction theory. We discuss their result in an operator-theoretic framework and prove that there are obstructions to its extension to operator-valued functions.
Integral formulae for special cases of Taylor's functional calculus
In this paper integral formulae, based on Taylor's functional calculus for several operators, are found. Special cases of these formulae include those of Vasilescu and Janas, and an integral formula for commuting operators with real spectra.
Isomorphic classification and lifting theorems for spaces of differentiable functions with Lipschitz conditions
-spectral factorization for rational matrix functions with alternative realization.
-Khintchine-Bonami inequality in free probability
We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length (). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.
Linearization of regular matrix polynomials.
Local polynomials are polynomials
We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.
Multiblock problems for almost periodic matrix functions of several variables.
Nevanlinna-Pick interpolation for Schur-Agler class functions on domains with matrix polynomial defining function in .
On decomposably regular operators.
On operator-valued analytic functions with positive real part whose logarithm belongs to a class
On some dilation theorems for positive definite operator valued functions
The aim of this paper is to prove dilation theorems for operators from a linear complex space to its Z-anti-dual space. The main result is that a bounded positive definite function from a *-semigroup Γ into the space of all continuous linear maps from a topological vector space X to its Z-anti-dual can be dilated to a *-representation of Γ on a Z-Loynes space. There is also an algebraic counterpart of this result.