Sentence examples for a given operator from inspiring English sources

This result is used to obtain a spectral characterization of the norm-closure of the class HC(H) of all hypercyclic operators acting on H, as well as a formula for the distance from a given operator to HC(H).

We describe a generalized version of Weyl′s principle and of the Heisenberg uncertainty principle under which the geometry and spectral theory of a given operator can be tied together to the geometry of its underlying space.

These off-diagonal bounds are obtained by a modification of Davies' technique suited to cope with operators in non-divergence form, and they also imply new results on the scale of Lq-spaces in which a given operator generates an analytic semigroup.

For 1≤p<∞ and a strictly pseudoconvex or bounded symmetric and circled domain D⊂Cn, we show that a given operator S on H2(D) is a Schatten-p-class perturbation of a Toeplitz operator if and only if T⁎θSTθ−S∈Sp for every inner function θ on D.

Let (T: Xto X) be a given operator.

Let ((X,d)) be a complete metric space and (T: Xto X) be a given operator.

Let K be a nonempty closed convex subset of a Banach space X, (A Ksubset X to X^) and (a Kto X) be two given operators.

Let (A Dsubseteq Xto X^) and (a Dto X) be given operators.

Let (A Kto X^) and (a K to X) be given operators.

Let (A Kto X^), (a Kto X) be the given operators.

Let (A Kto X^) and (a Kto X) be two given operators.