Sentence examples for class perturbation from inspiring English sources
Later Krein [42] generalized the trace formula to a considerably more general situation when A is an arbitrary self-adjoint operator and B is a trace class perturbation of A. Let A be a self-adjoint operator on Hilbert space and let B be a perturbed self-adjoint operator with (A-Bin {varvec{S}}_1).
The case of relative trace class perturbations is also considered.
This formula is extended to the case of relatively trace class perturbations.
More precisely, we prove that the spectral shift function integrated with respect to the spectral parameter from −∞ to λ (from λ to +∞) is concave (convex) with respect to trace class perturbations.
On the other hand, it can be shown that a function f preserves trace class perturbations, i.e., begin{aligned} A-Bin {varvec{S}}_1quad Longrightarrow quad f(A -f B in {varvec{S}}_1 end{aligned} (1.6.2 if and only if f is operator Lipschitz (the operators A and B do not have to be bounded).
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.
The representations of the group of unitary operators which are trace-class perturbations of the identity on an infinite-dimensional separable Hilbert space are classified according to factoriality, quasi-equivalence, and semifiniteness, by relating these representations to the quasi-free representations of the Weyl algebra.
In this work we presented TRANSWESD, an elaborated variant of transitive reduction, which is applicable to an extended class of perturbation graphs, i.e. cyclic, signed and weighted digraphs.
The class of perturbations generalizes the well-known "opening node" perturbation of Teichmüller theory.
The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations.
The gains for the observer are designed in order to compensate a more general class of perturbations that appear in the suggested glucose-insuline nonlinear model.
