18 citations · 27 across the 18 of their papers we have counts for
18 papers
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…
Generalized gyrovector spaces revisited
Toshikazu Abe, Osamu Hatori
We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.
The Mazur-Ulam property for a Banach space which satisfies a separation condition
Osamu Hatori
We study -rich spaces, lush spaces, and -extremely regular spaces concerning with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform algeb…
The Mazur-Ulam property for uniform algebras
Osamu Hatori
We give a sufficient condition for a Banach space with which the homogeneous extension of a surjective isometry from the unit sphere of it onto another one is real-linear. The cond…
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…
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…