Resolvents and Yosida approximations of displacement mappings of isometries

Continuity of the Yosida Approximants Corresponding to General Duality Mappings

Let $X$ be a real locally uniformly convex Banach space and $X^*$ be the dual space of $X$. Let $φ:\mathbf R_+\to \mathbf R_+$ be a strictly increasing and continuous function such that $φ(0) = 0$, $φ(r) \to \infty$ as $r\to\infty$, and let $J_φ$ be the duality mapping corresponding to $φ$. We will prove that for every $R>0$ and every $x_0\in X$ there exists a nondecreasing function $ψ= ψ(R, x_0) :\mathbf R_+\to \mathbf R_+$ such that $ψ(0) = 0$, $ψ(r)>0$ for $r>0$, and $\langle x^*- x_0^*, x-x_0\rangle \ge ψ(\|x-x_0\|) \|x-x_0\|$ for all $x$ satisfying $\|x-x_0\|\le R$ and all $x^*\in J_φx$ a…

对一组等距同构不变的单调算子与 Lipschitz 映射的延拓

Extension of monotone operators and Lipschitz maps invariant for a group of isometries

本文研究对等距同构不变的单调算子与 Lipschitz 映射，证明其保持不变性的极大延拓存在，并推广到保测 $L^p$ 情形及律不变相关对象。

Weighted Composition Groups on the Little Bloch space

We determine both the semigroup and spectral properties of a group of weighted composition operators on the Little Bloch space. It turns out that these are strongly continuous groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the infinitesimal generator as well as the resulting resolvents which are given as integral operators. As consequences, we complete the analysis of the adjoint composition group on the predual on the nonreflexive Bergman space, and a group of isometries associated with a specific automorphism of the upper half plane.