Sentence examples for be a separable complex from inspiring English sources

Let ((X,mu)) be a measure space and let E be a separable complex Hilbert space.

Throughout this paper let be a separable complex Hilbert space with inner product.

Let ℋ be a separable complex Hilbert space and be the set of complex numbers.

Let ({mathcal H}) be a (separable, complex) Hilbert space and take either (X={mathcal H}) or (X={mathcal L}({mathcal H})) and suppose that begin{aligned} {mathcal M}_t(x) = iA t)x end{aligned} (17.2) where A t) is a norm continuous map to the bounded self-adjoint operators on ({mathcal H}).

(b) Let ({mathcal H}) be a (separable, complex) Hilbert space and take either (X={mathcal H}) or (X={mathcal L}({mathcal H})) and suppose that begin{aligned} {mathcal M}_t(x) = iA t)x end{aligned} (17.2) where A t) is a norm continuous map to the bounded self-adjoint operators on ({mathcal H}).

Let H be a separable complex Hilbert space and the mapping F: ℝ → H be exponential then either F ≡ 0 or there exist a positive integer N such that F ( x ) = ∑ n = 1 N exp ( A n ( x ) + a n ( x ) ) e n. for all x ∈ H where A n : ℝ → ℝ is an additive function and a n is a function satisfying (1) for n = 1, 2,..., N. Proof.

Furthermore, in the case where X= Y is a separable complex Hilbert space, such a map is a small perturbation of an automorphism or an anti-automorphism.

We consider a Gelfand triple (E'rightarrow Hrightarrow E), so that E is a separable complex Banach space with dual (E'), and H is its dense Hilbert subspace.

Let $K \subset L$ be a separable algebraic extension.

Let H be a separable Hilbert space.

Let be a separable Banach space.