It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

Let τ be a conjugation, alias a conjugate linear isometry of order 2, on a complex Banach space X and let Xτ be the real form of X of τ -fixed points. In contrast to the Dunford–Pettis property, the alternative Dunford–Pettis property need not lift from Xτ to X. If X is a C*-algebra it is shown that Xτ has the alternative Dunford–Pettis property if and only if X does and an analogous result is ...

We prove that every surjective isometry from the unit sphere of a rank-2 Cartan factor C onto real Banach space Y, admits an extension to linear Y. The conclusion also covers case in which is spin factor. This result closes open problem and, combined with previous paper, allows us establish $$\hbox {JBW}^*$$ -triple M satisfies Mazur–Ulam property, is, its arbitrary Y

When C ⊆ F is a linear code over a finite field F, every linear Hamming isometry of C to itself is the restriction of a linear Hamming isometry of F to itself, i.e., a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping C to itself is an additive Hamming isometry, but there exist additive Hamming isometries that are...

Let V be an n-dimensional vector space over a finite field Fq and P = {1, 2, . . . , n} a poset. We consider on V the poset-metric dP . In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP ), for any poset-metric dP . We show that a linear isometry induces an automorphism of order in poset P , and consequently we show the existence of a pair of...

A map T: Ej —► E2 (E|, E2 Banach spaces) is an e-isometry if III T(X) T(Y)\\ \\X Y\\ I < e whenever X, Ye Ex. The problem of uniformly approximating such maps by isometries was first raised by Hyers and Ulam in 1945 and subsequently studied for special infinite dimensional Banach spaces. This question is here broached for the class of finite dimensional Banach spaces. The only positive homogene...

Given two complex Hilbert spaces H and K, let S(B(H)) and S(B(K)) denote the unit spheres of the C∗-algebras B(H) and B(K) of all bounded linear operators on H and K, respectively. We prove that every surjective isometry f : S(B(K)) → S(B(H)) admits an extension to a surjective complex linear or conjugate linear isometry T : B(K) → B(H). This provides a positive answer to Tingley’s problem in t...

Every isometry of a finite dimensional euclidean space is a product of reflections and the minimum length of a reflection factorization defines a metric on its full isometry group. In this article we identify the structure of intervals in this metric space by constructing, for each isometry, an explicit combinatorial model encoding all of its minimal length reflection factorizations. The model ...