Operators Commuting with Positive Operators

On Commuting Differential Operators

The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...

Essentially Commuting Toeplitz Operators

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

Commuting aggregation operators

We will investigate so-called commuting operators and their relationship to bisymmetry and domination. In the case of bisymmetric aggregation operators we will show a sufficient condition ensuring that two operators commute, while for bisymmetric aggregation operators with neutral element we will even give a full characterization of commuting n-ary operators by means of unary commuting operators.

Commuting Contractive Operators

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

Differential Operators Commuting with Invariant Functions