Osamu Hatori

most citedMultiplicatively spectrum-preserving and norm-preserving maps between invertible groups of commutative Banach algebras

18 citations · 22 across the 6 of their papers we have counts for

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6 papers · 1 filter

math.FA2009

A local Mazur-Ulam theorem

Osamu Hatori

We prove a local version of the Mazur-Ulam theorem.

math.FA2009★ 1 cited

Linear extensions of isometries between groups of invertible elements in Banach algebras

Osamu Hatori

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the invertible group $A^{- 1}$ of a unital Banach algebra $A$ onto an open subgroup of the invertible…

math.FA2009

An algebraic property of an isometry between the groups of invertible elements in Banach algebras

Osamu Hatori

We show that if $T$ is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then $T$ is extended to a surjective real-linear isometry up to trans…

math.FA2009★ 3 cited

Polynomially spectrum-preserving maps between commutative Banach algebras

Osamu Hatori, Takeshi Miura, Hiroyuki Takagi

Let $A$ and $B$ be unital semi-simple commutative Banach algebras. In this paper we study two-variable polynomials $p$ which satisfy the following property: a map $T$ from $A$ onto…

math.FA2009

Isometries between groups of invertible elements in Banach algebras

Osamu Hatori

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open s…

math.FA2009★ 18 cited

Multiplicatively spectrum-preserving and norm-preserving maps between invertible groups of commutative Banach algebras

Osamu Hatori, Takeshi Miura, Hiroyuki Takaggi

Let $A$ and $B$ be unital semisimple commutative Banach algebras and $T$ a map from the invertible group $A^{- 1}$ onto $B^{- 1}$ . Linearity and multiplicativity of the map are not a…