Generalizations of bornological convergence and convergence of partial maps via ideal

关于弧光滑映射的空间

On spaces of arc-smooth maps

本文研究了弧光滑映射空间的性质，证明了在适当闭集上，函数空间的集论恒等式在自然的局部凸拓扑下是Born学同构，并扩展到映射值域为方便向量空间的情况，获得相应的指数定律。

Duality for ideals of Lipschitz maps

We develop a systematic approach to the study of duality for ideals of Lipschitz maps from a metric space to a Banach space, inspired by the classical theory that relates ideals of operators and tensor norms for Banach spaces, by using the Lipschitz tensor products previously introduced by the same authors. We first study spaces of Lipschitz maps, from a metric space to a dual Banach space, that can be represented canonically as the dual of a Lipschitz tensor product endowed with a Lipschitz cross-norm. We show that several known examples of ideals of Lipschitz maps (Lipschitz maps, Lipschitz …

Convergence of Partial maps via bornology through ideal and its Characterization

In this paper we consider the idea of I - convergence of nets of partial function from a metric space (X; d) to a metric space (Y; ?) and derive several basic characterization. This idea extends the concept of convergence of nets of partial function introduced by G. Beer et.al [1].

A family of quotient maps of $\ell^\infty$ that do not admit uniformly continuous right inverses

Previously only two examples of Banach space quotient maps which do not admit uniformly continuous right inverses were known: one due to Aharoni and Lindenstrauss and one due to Kalton ($\ell^\infty\to\ell^\infty/c_{0}$). We show through an application of Kalton's Monotone Transfinite Sequence Theorem that a quotient map of a subspace of $\ell^\infty$ of sequences that converge to zero along an ideal in $\mathbb{N}$ toward another such subspace, provided one of the ideals is `much larger' than the other, cannot have a uniformly continuous right inverse. We show in general that pairs of ideals …

局部自同构算子理想上的乘法映射

Multiplicative maps on ideals of operators which are local automorphisms

本文给出了关于$C^*$ -代数B（H）的自同构群的自反性结果，H是可分的希尔伯特空间.设$ϕ:B(H)\to B(H)$是一个乘法映射（不假设线性或连续性），它在每一点都可以用算子范数中B（H）的自同构（当然，这些自同构可能依赖于点）来近似。则$ϕ$是代数B（H）的自同构.

半单巴拿赫代数上的可逆保持线性映射

Invertibility preserving linear maps on the semi-simple Banach algebras

本文证明了半单巴拿赫代数A的理想B的根的本质性意味着A上的任何可逆保持同构都是Jordan同态。特别是...