Decompositions of non-contractive operator-valued representations of Banach algebras
Boundedness in dilation theory
Note on a general dilation theorem
Some spectral properties of operator-valued representations of function algebras
Existence theorems for discrete boundary problems
On interpolation of completely monotonic sequences
Kato-Protter type inequalities, bounded vectors and the exponential function
Note on the existence of periodic solutions of a second order differential equation
The Hadamard product and related dilations
Sur les solutions périodiques d'une équation différentielle ordinaire d'ordre n
-vectors and boundedness
The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.
Componentwise and Cartesian decompositions of linear relations
Let A be a, not necessarily closed, linear relation in a Hilbert space ℌ with a multivalued part mul A. An operator B in ℌ with ran B ⊥ mul A** is said to be an operator part of A when A = B +̂ ({0} × mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for an operator part are established via the so-called...
Włodzimierz Mlak (1931-1994)
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