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Isometries of absolutely continuous function spaces with respect to the sum-norm
In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary...
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Circumcenter extension maps for non-positively curved spaces
We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a map, called circumcenter extension,...
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Isometry and phase-isometry of non-Archimedean normed spaces
In this paper, we study isometries and phase-isometries of non-Archimedean normed spaces. We show that every isometry f : S r ( X ) → S r ( X ), where X is...
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Properties of Hyperbolic Geometry
The previous chapter dealt almost exclusively with the problem of constructing various models of the hyperbolic plane and hyperbolic 3-space and...
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On Invertible m-isometrical Extension of an m-isometry
We give necessary and sufficient conditions on an m -isometry to have an invertible m -isometrical extension. As particular cases, we give a useful...
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Left-Invertibility of Rank-One Perturbations
For each isometry V acting on some Hilbert space and a pair of vectors f and g in the same Hilbert space, we associate a nonnegative number...
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On the Geometry of Finite Homogeneous Subsets of Euclidean Spaces
This survey is devoted to results recently obtained on finite homogeneous metric spaces. One of the main subjects of discussion is the classification...
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Spectral continuity and the dynamics of quasi-2-isometric operators
Linear dynamics has been a rapidly evolving area since the early 1990s. It lies at the intersection of operator theory and topological dynamics and...
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Envelopes in Banach spaces
We introduce the notion of isometric envelope of a subspace in a Banach space, establishing its connections with several key elements: (a) we explore...
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Rochberg’s Abstract Coboundary Theorem Revisited
Rochberg’s coboundary theorem provides conditions under which the equation...
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Conjugate Plateau Constructions in Product Spaces
This survey paper investigates, from a purely geometric point of view, Daniel’s isometric conjugation between minimal and constant mean curvature...
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Mathematics of 2-Dimensional Lattices
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by...
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On Perturbed Isometries Between the Positive Cones of Certain Continuous Function Spaces
Let X , Y be two compact Hausdorff perfectly normal spaces (in particular, compact metrizable spaces), C ( X ) be the real Banach space of all continuous...
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Quantum Codes Over an Extension of \({\mathbb {Z}_4}\)
Let \(\mathfrak {A}=\mathbb Z_4+u\mathbb Z_4+v\mathbb Z_4,\)...
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