Sentence examples for be a normal operator from inspiring English sources

Let be a normal operator commuting with Then (1.8).

Corollary 1 Let A be a normal operator commuting with B. Then w ( A B ) ≤ w ( A ) w ( B ). (1.9).

Let A be a normal operator in a Hilbert space H, and let G⊂H be a countable set of vectors.

Let M be a normal operator with discrete spectrum; and all its eigenvalues, which lie in the corner (psi_{2theta}= { lambda: vert varphi vert <2theta } ) ((0

end{aligned}Here N is a normal operator and (E_N) is its spectral measure.

Indeed, if N is a normal operator, then ({text {Re}}N) and ({text {Im}}N) are commuting self-adjoint operators.

On the other hand, if A and B are commuting self-adjoint operators, then (A+mathrm{i}B) is a normal operator.

Since N is a normal operator on the Hilbert space H, then ∥ N j x ∥ 2 = 〈 | N j | 2 x, x 〉 = 〈 | N | 2 j x, x 〉. for any j ∈ { 0, …, n } and for any x ∈ H with ∥ x ∥ = 1.

for any x, y ∈ H. Proof If N is a normal operator, then for any j ∈ N, we have that | N j | 2 = ( N ∗ N ) j = | N | 2 j.

Theorem 2.18 Let α 1, α 2 ∈ ( 0, 1 ) and P be a normal cone, operator A : P → P is α 1 -concave, operators B 1, B 2 satisfy the conditions of Corollary  2.10, where B 1 is α 2 -concave.

For a Hilbert space operator A, that is not a normal operator, we give some necessary conditions on the thickness of the spectrum of A for C∗(A) to have a subnormal generator.