4 citations · 5 across the 15 of their papers we have counts for
16 papers
Order isomorphisms on positive cones of non-unital -algebras
Osamu Hatori, Shiho Oi
Let and be -algebras, not necessarily unital, and let be a positively homogeneous order isomorphism. We first prove that is additive and extends uni…
Surjective Fischer--Muszély maps on positive cones of JB-algebras
Osamu Hatori, Shiho Oi
We prove that every surjective Fischer--Muszély map between positive cones of arbitrary JB-algebras is additive and positively homogeneous, and extends uniquely to a bounded positi…
Linear maps preserving families of C-symmetric operators
Mayu Anzai, Shiho Oi
Let $\cH$ be a separable complex Hilbert space with $\dim\cH\ge3$. We characterize the bounded bijective complex-linear maps on $\BH$ for which there exists a bijection of…
Spectral decomposition of doubly power-bounded elements in Banach algebras
Osamu Hatori, Shiho Oi
We establish a characterization of doubly power-bounded elements with finite spectrum in Banach algebras. In particular, we present a spectral decomposition for such elements, exte…
Spectrally additive maps on the positive cones of the Wiener algebra
Shiho Oi, Kaito Sato
We study surjective maps between the positive cones of the Wiener algebra that preserve the spectrum of the sum of every two elements. We show that such maps can be extended to iso…
Spectral decomposition of power-bounded operators: The finite spectrum case
Shiho Oi, Jyamira Oppekepenguin
In this paper, we investigate power-bounded operators, including surjective isometries, on Banach spaces. Koehler and Rosenthal asserted that an isolated point in the spectrum of a…
Multiplicatively spectrum-preserving maps on -algebras
Michiya Mori, Shiho Oi
We study surjective maps between the sets of all self-adjoint elements of unital -algebras which satisfy the multiplicatively spectrum-preserving property. We show that such m…
Non-linear characterization of Jordan -isomorphisms via maps on positive cones of -algebras
Osamu Hatori, Shiho Oi
We study maps between positive definite or positive semidefinite cones of unital -algebras. We describe surjective maps that preserve (1) the norm of the quotient or multiplic…
Isometries between groups of invertible elements in Fourier-Stieltjes algebras
Osamu Hatori, Shiho Oi
We prove that if open subgroups of the groups of invertible elements in two Fourier-Stieltjes algebras are isometric as metric spaces, then the underlying locally compact groups ar…
Linear preservers on idempotents of Fourier algebras
Ying-Fen Lin, Shiho Oi
In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an ope…
Jordan -homomorphisms on the spaces of continuous maps taking values in -algebras
Shiho Oi
Let be a unital -algebra. We consider Jordan -homomorphisms on and Jordan -homomorphisms on . More…
Isometries and hermitian operators on spaces of vector-valued Lipschitz maps
Shiho Oi
We study hermitian operators and isometries on spaces of vector-valued Lipschitz maps with the sum norm: . There are two main theorems in this paper. F…
Tingley's problem on uniform algebras
Osamu Hatori, Shiho Oi, Rumi Shindo Togashi
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…
A generalization of the Kowalski -S\{l} odkowski theorem and its application to 2-local maps on function spaces
Shiho Oi
In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski theorem due to Li, Peralta, Wang and Wang. As a corollary, we prove that every 2-local map in the set of…
2-local isometries on function spaces
Osamu Hatori, Shiho Oi
We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in…
Isometries on Banach algebras of vector-valued maps
Osamu Hatori, Shiho Oi
We propose a unified approach to the study of isometries on algebras of vector-valued Lipschitz maps and those of continuously differentiable maps by means of the notion of admissi…