Sentence examples for bounded operators in the from inspiring English sources

More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology.

We define a two-parameter scale of Banach spaces contained in the contininuous functions on the space of probability measures on a compact metric space X, and show that the resolvent of the Fleming-Viot process is a bounded operator in the scale.

Therefore, is a bounded operator in the space of.

Throughout this paper, we assume that (A D(A)subset Eto E) is a closed linear operator and −A generates a uniformly bounded (C_{0} -semigroup (T(t)) ((tgeq0} -semigroup (M=sup_{T t [0,+inftgeq0 T(t)|_{mathcal{L}(E)}), where (mathcal{L}(E)) stands fon thE.Banach space of aLetlinear and bounded operators in E. For M=sup_{tinls of the theory of operator semigroups, see [04].

The main theorem is proven on the level of semigroups of bounded operators in F so it can be used in a wider context due to its generality.

We develop criteria for the natural scalar product in the associated representation spaces to be positive definite and for the relations to have representations by bounded operators in a Hilbert space.

A particular state may then be used to specify a concrete representation of the algebra as a set of bounded operators in a Hilbert space.

In what follows we shall describe some asymptotic formulas for the commutators defined by the values of the analytic functional calculus of some commutingn-tuple of bounded operators in a complex Banach space.

Let S be a locally compact abelian semigroup and T a bounded representation of S by linear bounded operators in a Banach space X, with spectrum Sp(T).

Let be bounded operators in.

Then, as Q is a bounded operator in L2, it follows from the relation for the resolvents of the operators L0 and L [[30], p. 219].