During the last years the dynamics of linear operators on infinite dimensional spaces has been extensively studied, see the survey articles [3], [6], [7], [8], [9], [11]. Let us recall the notion of hypercyclicity. Let X be a separable Banach space and T : X → X be a bounded linear operator. The operator T is said to be hypercyclic provided there exists a vector x ∈ X such that its orbit under ...

We prove a variant of Krein’s resolvent formula for self-adjoint extensions given by arbitrary boundary conditions. A parametrization of all such extensions is suggested with the help of two bounded operators instead of multivalued operators and selfadjoint linear relations.

We extend the results of Mary Embry [9] on majorisation and range inclusion of bounded linear operators on Banach spaces to the case when one of the two operators is a convex process. An application in controllability is given.

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.

In his book [14], Wong studies the properties of pseudodifferential operators arising in quantummechanics, first envisaged byWeyl [13], as bounded linear operators on L2(Rn) (the space of square integrable functions on Rn with respect to the Lebesgue measure). For this reason, M. W. Wong calls the operators treated in his book Weyl transforms. Here, we consider the singular partial differential...

It is well known that the Hilbert tranformation and the conjugate function operator restricted to even (odd) functions define bounded linear operators on weighted If spaces under more general conditions than is the case for the unrestricted operators. In analogy with recent results of Hunt, Muckenhoupt and Wheeden for the Hilbert transform and the conjugate function operator, we obtain necessar...

Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition, we present some results which adapt to asymptotic case the classic results.

In this paper we obtained mean ergodic theorems for semigroups of bounded linear or continuous affine linear operators on a Banach space under non-power bounded conditions. We then apply them to the wave equation and the system of elasticity to show that the mean of their solutions converges to their equilibriums.

Given bounded linear operators T1, T2 and T3, this paper investigates certain invariance properties of the operator product T1XT3 with respect to the choice of bounded linear operator X, where X is a generalized inverse of T2. Different types of generalized inverses are taken into account.