Generators of semigroups on Banach spaces inducing holomorphic semiflows

子半流上的Oseledets分解

Oseledets Decomposition on Sub semiflows

本文在Banach空间的连续嵌入子空间上证明了Oseledets分解的存在性，并给出了适用于微分方程生成动力系统的自然假设条件。

Recurrent strongly continuous operator families on Banach space

In this paper, we analyze recurrent $C_{0}$-semigroups of bounded operators on Banach spaces. We also introduce the notion of a (uniformly) $C_{0}$-rigid semigroups of bounded operators and give a structural characterization of them. A characterization of a Li-Yorke chaoticity of the translation semigroup $(T(t))_{t\geq 0}$ on weighted spaces of integrable functions and continuous functions in terms of admissible weight function is given. The recurrent $C_0$-semigroups induced by semiflows are characterized on the spaces of integrable functions and of spaces of continuous functions.

A Desch-Schappacher perturbation theorem for bi-continuous semigroups

We prove a Desch-Schappacher type perturbation theorem for one-parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this paper we chose to work in the framework of bi-continuous semigroups. This choice has the advantage that we can treat in a unified manner two important classes of semigroups: implemented semigroups on the Banach algebra $\mathscr{L}(E)$ of bounded, linear operators on a Banach space $E$, and semigroups on the space of bounded and continuous functions over a Polish space induced by jointly continuous…

Banach-Stone-like results for combinatorial Banach spaces

We show that under a certain topological assumption on two compact hereditary families $\F$ and $\G$ on some infinite cardinal $κ$, the corresponding combinatorial spaces $X_\F$ and $X_\G$ are isometric if and only if there is a permutation of $κ$ inducing a homeomorphism between $\F$ and $\G$. We also prove that two different regular families $\F$ and $\G$ on $ω$ cannot be permuted one to the other. Both these results strengthen the main result of \cite{BrechFerencziTcaciuc}.

连续函数空间及其子空间上的加权复合半群

Weighted composition semigroups on spaces of continuous functions and their subspaces

本文研究连续函数 Banach 空间及其子空间上由半流和半余循环诱导的加权复合半群，证明其在混合拓扑下可非平凡强连续，并给出强连续性、生成元及相关空间的刻画。

Characterizations of weakly $\mathcal{K}$-analytic and Vašák spaces using projectional skeletons and separable PRI

We find characterizations of Vašák spaces and weakly $\mathcal{K}$-analytic spaces using the notions of separable projectional resolution of the identity (SPRI) and of projectional skeleton. This in particular addresses a recent challenge suggested by M. Fabian and V. Montesinos in \cite{FM18}. Our method of proof also gives similar characterizations of WCG spaces and their subspaces (some aspects of which were known, some are new). Moreover we show that for countably many projectional skeletons $\{\mathfrak{s}_n: n \in ω\}$ on a Banach space inducing the same set, there exists a projectional …