Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem

The structure of maps on the space of all quantum pure states that preserve a fixed quantum angle

Let $H$ be a Hilbert space and $P(H)$ be the projective space of all quantum pure states. Wigner's theorem states that every bijection $ϕ\colon P(H)\to P(H)$ that preserves the quantum angle between pure states is automatically induced by either a unitary or an antiunitary operator $U\colon H\to H$. Uhlhorn's theorem generalises this result for bijective maps $ϕ$ that are only assumed to preserve the quantum angle $\fracπ{2}$ (orthogonality) in both directions. Recently, two papers, written by Li--Plevnik--Šemrl and Gehér, solved the corresponding structural problem for bijections that preserv…

里斯空间中的抽象不定问题及其应用

Abstract Indefinite Problems in Riesz Spaces with Its Applications

研究希尔伯特空间\(X\)（连续嵌入巴拿赫格\(E\)）上泛函临界点存在性，通过构造格分解获空间分解，结合下降流不变集法与莫尔斯理论得抽象不定问题多临界点存在性，最后应用于椭圆边值问题。

具有不定二度量的空间的构造及其应用

Construction of Spaces with an Indefinite two-Metric and Applications

本文引入二-Krein空间概念，从经典Krein空间构造具有不定二内积的空间，推广基本分解、基本对称性与范数等价性等结果，并研究其中的强有界变差函数及其二范数结构。

投影几何与松弛拟正交性：用于inf-sup稳定Galerkin方法

Projection geometry and relaxed quasi-orthogonality for inf-sup stable Galerkin methods

本文证明一致inf-sup稳定的嵌套Petrov-Galerkin方法满足松弛拟正交性，并构造反例说明完全拟正交性需额外层次信息。