Given Banach spaces X, Y and a compact Hausdorff space K, we use polymeasures to give necessary conditions for a multilinear operator from C(K, X) into Y to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for X to have the Schur property (resp. to contain no copy of c0), and for K to be scattered. This extends results concerning linear ...

We consider the event-triggered control of continuous-time linear infinite-dimensional systems. We show that an event trigger that measures the difference of a control input leads to the positive minimum inter-event time if a feedback operator is compact. Moreover, under certain natural assumptions on the infinite-dimensional system, we show that there exists an event trigger such that the clos...

Non-linear Fourier analysis on compact groups is used to construct an orthonormal basis of the physical (gauge invariant) Hilbert space of Hamiltonian lattice gauge theories. In particular, the matrix elements of the Hamiltonian operator involved are explicitly computed. Finally, some applications and possible developments of the formalism are discussed. CPT-99/P.3856 University of Parma Prepri...

The aim of the present paper is to define compact operators on asymmetric normed spaces and to study some of their properties. The dual of a bounded linear operator is defined and a Schauder type theorem is proved within this framework. The paper contains also a short discussion on various completeness notions for quasi-metric and for quasi-uniform spaces. AMS 2000 MSC: Primary: 47B07; Secondar...

approximation error A linear operator L H H on a Hilbert space H is said to be self adjoint if for all f g H hLf gi hf Lgi It is said to be positive resp strictly positive if it is self adjoint and for all non trivial f H hLf fi resp hLf fi The next result the Spectral Theorem for compact operators see Section of for a proof will be useful in this and the next chapter Theorem Let L be a compact...

We prove compact-randomness of the intersection of a measurable familyof compact-random sets. This generalizes results on the intersection of countable families of random sets. The main tools are given by the theory of Souslin spaces and the idea of countable separation. An example of a random set is given by the energy spectrum of an electron in a disordered solid, or more generally by the spe...

In this note, we show that the operator theoretic concept of Kolmogorov numbers and the number of degrees of freedom at level ǫ of a communication channel are closely related. Linear communication channels may be modeled using linear compact operators on Banach or Hilbert spaces and the number of degrees of freedom of such channels is defined to be the number of linearly independent signals tha...

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.