Sentence examples for bounded continuous field of from inspiring English sources

Let ((A_{t})_{t in Omega }) be a bounded continuous field of positive operators in (mathbb {A}).

We can easily generalize the above results to a bounded continuous field of self-adjoint elements in a unital (C^ -algebra ({mathC^ -algebra

Theorem 1 Let ( x t ) t ∈ T be a bounded continuous field of self-adjoint elements in a unital C ∗ -algebra defined on a locally compact Hausdorff space T equipped with a bounded Radon measure μ.

(ii) Using the same technique as in Remark 2, we can obtain generalizations of the above results for a bounded continuous field of self-adjoint elements in a unital (C^ -algebra.

Moreover, Hansen et al. [7] presented a general formulation of Jensen's operator inequality for a bounded continuous field of self-adjoint operators and a unital field of positive linear mappings: f ( ∫ T ϕ t ( x t ) d μ ( t ) ) ≤ ∫ T ϕ t ( f ( x t ) ) d μ ( t ), (3).

Let ( x t ) t ∈ T be a bounded continuous field of self-adjoint elements in a unital C ∗ -algebra with the spectra in [ m, M ], m < M, defined on a locally compact Hausdorff space T equipped with a bounded Radon measure μ, and let ( ϕ t ) t ∈ T be a unital field of positive linear maps ϕ t : A → B from to another unital C ∗ -algebra ℬ.

holds for every bounded continuous field ( A t ) t ∈ T of self-adjoint elements in A with spectra contained in J. Proof We consider the unital positive linear map Ψ : C ( T, A ) ⟶ B defined by Ψ ( ( A t ) t ∈ T ) = ∫ T Φ t ( A t ) d μ ( t ).

Let (resp., ) denote the collection of all -valued bounded continuous functions (resp., the class of jointly bounded continuous functions ).

Throughout the rest of this paper, let (resp., ) be the space of bounded continuous (resp., jointly bounded continuous) functions with supremum norm, and (1.8).

The C∗-algebra of bimodule mappings with a right adjoint is a continuous field of finite dimensional C∗-algebras over a compact Hausdorff space, whose fiber dimensions are bounded above by the index.

where is the set of bounded continuous n-vector functions on Now, define as the subsequent bounded continuous function: (2.5).