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Define a operator on as follows: (2.13).
That is, is a class A operator on.
Assume that ran is not dense, then is a class A operator on and.
Theorem 3.3 Let A and B ∈ B ( H ). Then Γ A, B is a ∗-class A operator on C 2 ( H ) if and only if A and B ∗ belong to ∗-class A operators.
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In classical physics an observable value is just a number; today a quantum mechanical observable value is defined as an operator on a Hilbert space.
The spectrum of a compact linear operator largely resembles the spectrum of an operator on a finite dimensional space.
Suppose T is an operator on a Fréchet space X.
Consider an operator on a manifold with boundary.
Enflo [11] constructed in 1976 the first example of an operator on a Banach space without nontrivial invariant subspaces.
Let T be an operator on a separable Banach space, and denote by σp(T) its point spectrum.
For each column of the table, there is a possibility to choose an operator on the column, for example, equal or not equal.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com