Isometries between groups of invertible elements in Banach algebras

• Autorzy: Osamu Hatori
• Języki publikacji: EN

Abstrakty

EN

We show that if T is an isometry (as metric spaces) from an open subgroup of the group of invertible elements in a unital semisimple commutative Banach algebra A onto a open subgroup of the group of invertible elements in a unital Banach algebra B, then $T(1)^{-1}T$ is an isometrical group isomorphism. In particular, $T(1)^{-1}T$ extends to an isometrical real algebra isomorphism from A onto B.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 3
• Strony: 293-304

Daty

wydano

2009

Twórcy

autor

Osamu Hatori

• Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181 Japan

Identyfikatory

DOI

10.4064/sm194-3-5