We survey the most recent results on the extension of isometries between special subsets of
the unit spheres of C*-algebras, von Neumann algebras, trace class operators, preduals of …

We prove that a surjective isometry between the unit spheres of two uniform algebras is
extended to a surjective real-linear isometry between the uniform algebras. It provides the …

Let (Ω, μ) be a σ-finite measure space. Given a Banach space X, let the symbol S (X) stand
for the unit sphere of X. We prove that the space L∞(Ω, μ) of all complex-valued measurable …

Abstract Let (Ω, A, μ) and (Γ, B, ν) be two arbitrary measure spaces, and p∈[1,∞]. Set S (L p
(μ))+:={f∈ L p (μ):‖ f‖ p= 1; f≥ 0 μ-ae}, that is, the positive part of the unit sphere of L p (μ) …

Given a C∗-algebra A, let S (A+) denote the set of positive elements in the unit sphere of A.
Let H 1, H 2, H 3, and H 4 be complex Hilbert spaces, where H 3 and H 4 are infinite …

Let M and N be von Neumann algebras, S (M)+ be the collection of all positive norm one
elements in M, and PM be the projection lattice of M. Let Φ: PM→ PN be a metric preserving …

In this paper, we study the problem of extending surjective isometries between the positive
unit spheres of two\((\sum\ell _p) _ {\ell _q}\)-spaces for\(1\le p, q\le\infty\). Let\(S_ {(\sum\ell …

In this paper, we study the extension problems of norm-additive maps between the positive
unit spheres of ℓ q (ℓ p), 1≤ p, q≤∞. Let S ℓ q (ℓ p)+={x∈ ℓ q (ℓ p): x≥ 0;‖ x‖= 1} be the …

Let Γ , Δ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} …

Let E and P be subsets of a Banach space X‎,‎ and let us define the unit sphere around E in P
as the set Sph (E; P)‎:‎=\left {x ∈ P‎:‎ ‖ xb ‖= 1 for all b ∈ E\right\}. Given a C^*-algebra A and …