The central aim of this paper is to study completely positive processeskwhich admit a differential description through a stochastic equation of the formdkt=kt∘θαβ Λβα(t), in whichΛis the matrix of basic integrators of finite dimensional quantum stochastic calculus, andθis a matrix of bounded linear maps on the algebra.
On the other hand, since is a bounded linear map on, then there exists a constant such that (2.41).
We also prove that if X is any infinite dimensional subspace of the space of continuous functions on a compact Hausdorff space, then there exists a bounded linear map on X which is not completely bounded.
If U is the commutant of a strictly cyclic unilateral weighted shift with a monotonically decreasing weight sequence, then we show that there is a natural isomorphism of the Banach space of bounded linear maps from U into B(H) with the Banach space of bounded linear maps of the trace class operators into H, where H is a separable, infinite dimensional Hilbert space.
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures.
Let be the space of all bounded linear mapping from to.
It follows from the controllability of system (1.2) that is a surjective bounded linear map.
Hence is a bounded linear map and therefore continuous.
The dilations for operator-valued measures (OVMs) and bounded linear maps indicate that the dilation theory is in general heavily dependent on the Banach space nature of the dilation spaces.
Moreover, throughout this paper we denote by bounded linear operators,,, bounded linear maps that represent the control action, and a map such that is continuous for each.
Let (A:H_{1}longrightarrow H_{3}) be a bounded linear mapping.
