Strictly semi-transitive operator algebras

On Banach spaces whose group of isometries acts micro-transitively on the unit sphere

We study Banach spaces whose group of isometries acts micro-transitively on the unit sphere. We introduce a weaker property, which one-complemented subspaces inherit, that we call uniform micro-semitransitivity. We prove a number of results about both micro-transitive and uniformly micro-semitransitive spaces, including that they are uniformly convex and uniformly smooth, and that they form a self-dual class. To this end, we relate the fact that the group of isometries acts micro-transitively with a property of operators called the pointwise Bishop-Phelps-Bollobás property and use some known r…

Compact convex sets that admit a lower semicontinuous strictly convex function

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with its weak$^*$ topology. In addition, we find exposed points where a strictly convex lower semicontinuous function is continuous.

Strictly elliptic operators with generalized Wentzell boundary conditions on continuous functions on manifolds with boundary

We prove that strictly elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups of angle $\fracπ{2}$ on the space of continuous function on a compact manifold with boundary.

Strictly Singular Uniform $λ-$Adjustment in Banach Spaces

Based on the recently introduced uniform $λ-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely strictly singular operators to the sequences of closed subspaces and operators in Banach spaces and prove theorems about lower semi--Fredholm stability. We also state some new open questions related to strict singularity and the geometry of Banach spaces.

Banach代数中的不相交F-半传递性

Disjoint F-semi-transitivity in Banach algebras

本文研究了由等距同构与左乘子复合的算子的不相交Furstenberg-半传递性，在非单位范数代数上刻画了不相交F-半传递和不相交超循环算子，并应用于加权双边移位和加权复合算子。

Non-unitarisable representations and maximal symmetry

We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique invariant complemented subspace. This is subsequently combined with rigidity results for the unitary representation of ${\rm Aut}(T)$ on $\ell_2(T)$, where $T$ is the countably infinite regular tree, to describe the possible bounded subgroups of ${\rm GL}(\mathcal H)$ extending a well-known non-unitarisable representation of $\mathbb F_\infty$. As a related re…