Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

Let Ω ⊂ ℝp, p ϵ ℕ* be a nonempty subset and B(Ω) be the Branch lattice of all bounded real functions on a Ω, equipped with sup norm. Let 𝑋 ⊂ 𝐵(Ω) be a linear sublattice of 𝐵(Ω) and 𝐴: 𝑋 → 𝑋 be a ...

Let (X, d) be a complete metric space. We prove that there is a continuous, linear extension operator from the space of all partial, continuous, bounded metrics with closed, bounded domains in X ...

This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

In the context of quantum physics, the term "duality" refers to transformations that link apparently distinct physical theories, often unveiling hidden symmetries. Some recent studies have been aimed ...