Derivations of Nest Algebras.
Derivative of the norm of a linear mapping and its application to differential equations
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
Des produits de Riesz comme mesures spectrales
Description lagrangienne d'un boson scalaire à l'aide d'un triplet nucléaire
Description of invariant subspaces of Lp(μ) by multiplication operators.
Description of the structure of singular spectrum for Friedrichs model operators near singular point.
Déterminant relatif et la fonction Xi
Determination of the Invariant Interval for Positive Linear Operators by a Nonstationary Iterative Procedure
Dichotomy and functional calculi.
Die absolute Stetigkeit des positiven Spektrums der Schwingungsgleichungen mit oszillierendem Hauptteil.
Different types of solvability conditions for differential operators.
Differentiability of perturbed semigroups and delay semigroups
Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in 1995 that immediate...
Differentiability of the g-Drazin inverse
If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z)g-Drazin invertible, we study conditions under which the g-Drazin inverse is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix-valued function and a result on differentiation of the Moore-Penrose inverse in Hilbert spaces.
Differentiable bundles of subspaces and operators in Banach spaces
Differentiable -functional calculus for certain sums of non-commuting operators
We consider a special class of sums of non-commuting positive operators on L²-spaces and derive a formula for their holomorphic semigroups. The formula enables us to give sufficient conditions for these operators to admit differentiable -functional calculus for 1 ≤ p ≤ ∞. Our results are in particular applicable to certain sub-Laplacians, Schrödinger operators and sums of even powers of vector fields on solvable Lie groups with exponential volume growth.
Differential analysis of matrix convex functions. II.
Differentiation of Banach-space-valued additive processes
Dilatability of sesquilinear form-valued kernels
Dilatations des commutants d'opérateurs pour des espaces de Krein de fonctions analytiques
Soient et deux espaces de Krein de fonctions analytiques dans le disque unité invariants pour l’opérateur de déplacement à gauche et soit un opérateur linéaire continu de dans dont l’adjoint commute avec . Nous étudions les dilatations de qui conservent cette propriété de commutation et pour lesquelles les formes hermitiennes définies par et ont le même nombre de carrés négatifs. Nous obtenons ainsi une version du théorème de dilatation des commutants d’opérateurs dans le cadre...
Dilations of Banach space operator valued functions