On nonlinear perturbations of isometries
From MaRDI portal
Publication:1906493
DOI10.1007/BF01461008zbMath0836.46014MaRDI QIDQ1906493
Publication date: 25 February 1996
Published in: Mathematische Annalen (Search for Journal in Brave)
inequalityuniform approximation\(\varepsilon\)-isometryreal Banach spacessurjective mapping preserving distance one
Normed linear spaces and Banach spaces; Banach lattices (46B99) Isometric theory of Banach spaces (46B04)
Related Items (66)
More on stability of almost surjective \(\varepsilon\)-isometries of Banach spaces ⋮ On the improvement of Fickett's theorem on bounded sets ⋮ Stability of \(\varepsilon\)-isometric embeddings into Banach spaces of continuous functions ⋮ Stability of \(\varepsilon\)-isometries on \(\mathcal{L}_\infty\)-spaces ⋮ Stability of a pair of Banach spaces for \(\varepsilon\)-isometries ⋮ A set-valued extension of the Mazur–Ulam theorem ⋮ Isosceles-orthogonality preserving property and its stability ⋮ Stability of a pair of Banach spaces for coarse Lipschitz embeddings ⋮ On universally left-stability of \(\varepsilon\)-isometry ⋮ Hyers-Ulam stability of isometries on bounded domains ⋮ On non-surjective \(\varepsilon\)-isometric embeddings between Hausdorff metric spaces of compact convex subsets ⋮ On the quasi-Figiel problem and extension of \(\varepsilon\)-isometry on unit sphere of \(\mathcal{L}_{\infty, 1^+}\) space ⋮ A universal inequality for stability of coarse Lipschitz embeddings ⋮ Non-surjective coarse isometries between \(L_p\) spaces ⋮ On linear isometries and \(\varepsilon\)-isometries between Banach spaces ⋮ Non-surjective coarse embeddings of continuous functions spaces ⋮ Hyers–Ulam stability of non-surjective isometries between subspaces of continuous functions ⋮ On the Figiel type problem and extension of \(\varepsilon\)-isometry between unit spheres ⋮ Coarse version of the Banach-Stone theorem ⋮ The slice approximating property and Figiel-type problem on unit spheres ⋮ On a universal inequality for approximate phase isometries ⋮ On perturbed isometries between the positive cones of certain continuous function spaces ⋮ On stability of almost surjective functional equations of uniformly convex Banach spaces ⋮ On the stability of the squares of some functional equations ⋮ Isometric Approximation in Bounded Sets and Its Applications ⋮ A note on the stability of nonsurjective 𝜖-isometries of Banach spaces ⋮ Hyers-Ulam stability of isometries and non-expansive maps between spaces of continuous functions ⋮ Stability of \(\varepsilon \)-isometries and their symmetrizations on the positive cones of \(c_0\) ⋮ Hyers-Ulam stability of isometries on bounded domains. II. ⋮ On perturbations of two general equations in several variables ⋮ \(\varepsilon\)-isometries between the positive cones of continuous functions spaces ⋮ Generalized stability of isometries ⋮ Hyers-Ulam stability of bijective \(\varepsilon\)-isometries between Hausdorff metric spaces of compact convex subsets ⋮ Stability characterizations of \(\epsilon\)-isometries on certain Banach spaces ⋮ Stability of \(\varepsilon\)-isometries on the positive cones of finite-dimensional Banach spaces ⋮ On weak stability of \(\varepsilon\)-isometries on wedges and its applications ⋮ On non-linear \(\varepsilon\)-isometries between the positive cones of certain continuous function spaces ⋮ Stability of symmetric \(\varepsilon \)-isometries on wedges ⋮ A convex set-valued version of the Mazur-Ulam theorem on Asplund spaces ⋮ On perturbed metric-preserved mappings and their stability characterizations ⋮ Isometric approximation property in Euclidean spaces. ⋮ On non-surjective coarse isometries between Banach spaces ⋮ Maps preserving unitarily invariant norms of Jordan product of matrices ⋮ Isometric approximation ⋮ On the symmetrizations of \(\epsilon \)-isometries on Banach spaces ⋮ A fixed point approach to the stability of isometries ⋮ On stability and weak-star stability of \(\varepsilon\)-isometries ⋮ On approximate isometries and application to stability of a functional equation ⋮ Stability of almost surjective \(\varepsilon\)-isometries of Banach spaces ⋮ On extension of isometries and approximate isometries between unit spheres ⋮ Hyers-Ulam stability of \(\epsilon\)-isometries between the positive cones of \(L^p\)-spaces ⋮ On approximate phase isometries ⋮ A note on stability of non-surjective \(\varepsilon \)-isometries between the positive cones of \(L^p\)-spaces ⋮ Hyers-Ulam stability of \(\varepsilon \)-isometries between the positive cones of \(c_0\) ⋮ Stability of surjectivity ⋮ ON HYPERSTABILITY OF ADDITIVE MAPPINGS ONTO BANACH SPACES ⋮ Superstability of the Cauchy, Jensen and isometry equations ⋮ Stability of the preservation of the equality of distance ⋮ Properties of isometric mappings ⋮ On \(\mathcal{U}\)-weak stability of coarse isometries between \(L^p\) spaces ⋮ Stability of Banach spaces via nonlinear \(\varepsilon\)-isometries ⋮ \(\epsilon\)-isometries in Euclidean spaces ⋮ Asymptotic properties of isometries. ⋮ A universal theorem for stability of \(\varepsilon\)-isometries of Banach spaces ⋮ Nonsurjective nearisometries of Banach spaces. ⋮ On non-\(L^0\)-linear perturbations of random isometries in random normed modules
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Approximate isometries of the space of continuous functions
- Approximately isometric and multiplicative transformations on continuous function rings
- Approximate Isometries on Finite Dimensional Banach Spaces
- Stability of Isometries
- Two Dimensional ɛ-Isometries
- Stability of Isometries on Banach Spaces
- Maps which preserve equality of distance
- On Isometries of Euclidean Spaces
- On approximate isometries
- Approximate isometries
This page was built for publication: On nonlinear perturbations of isometries
