Tensor products of linear operators in locally convex spaces
The arithmetic-geometric mean and its generalizations for noncommuting linear operators
The calculus of operator functions and operator convexity [Book]
The Cayley transform of Banach algebras.
The Fréchet derivative of an analytic function of a bounded operator with some applications.
The monogenic functional calculus
A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.
The product of relatively regular operators
The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)
Kato’s conjecture, stating that the domain of the square root of any accretive operator with bounded measurable coefficients in is the Sobolev space , i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.
The spectral mapping theorem for one-parameter groups of positive operators on C0(X).
The spectral mapping theorem for the essential approximate point spectrum
The Weyl correspondence as a functional calculus
The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.
Théorie spectrale