Sectorial operators with convolution term

Sectorial Operators and Interpolation Theory

We present a survey of recent applications of interpolation ideas in the study of sectorial operators.

Continuityof Operators Intertwiningwith Convolution Operators

Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let Tm be the corresponding convolution operator on LðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F : X ! LðGÞ such that FS 1⁄4 TmF is continuous if and only if the pair ðS;TmÞ has no critical eigenvalue. # 2002 Elsevier Sci...

Sofic groups and convolution operators

Conjecture: Let Γ be a discrete group, f ∈ L(Γ) and Tf : L (Γ) → L(Γ) be the right convolution by f . Then if Tf is injective, it is surjective as well. We prove the conjecture for the class of sofic groups. AMS Subject Classification: 43A20

Generation of Equicontinuous Semigroups by Hermitian and Sectorial Operators. I

REAL INTERPOLATION OF DOMAINS OF SECTORIAL OPERATORS ON Lp-SPACES

Let A be a sectorial operator on a non-atomic Lp-space, 1 ≤ p < ∞, whose resolvent consists of integral operators, or more generally, has a diffuse representation. Then the fractional domain spaces D(Aα) for α ∈ (0, 1) do not coincide with the real interpolation spaces of (Lq , D(A)). As a consequence, we obtain that no such operator A has a bounded H∞-calculus if p = 1.