Displaying similar documents to “Isometries of the unitary groups in C*-algebras”

Isometries between groups of invertible elements in C*-algebras

Osamu Hatori, Keiichi Watanabe (2012)

Studia Mathematica

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We describe all surjective isometries between open subgroups of the groups of invertible elements in unital C*-algebras. As a consequence the two C*-algebras are Jordan *-isomorphic if and only if the groups of invertible elements in those C*-algebras are isometric as metric spaces.

Nonassociative real H*-algebras.

Miguel Cabrera, José Martínez Aroza, Angel Rodríguez Palacios (1988)

Publicacions Matemàtiques

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We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution τ such that A = {b ∈ B : τ(b) = b*}. Using this, we obtain our main result, namely: (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically isomorphic.

On a method of determining supports of Thoma's characters of discrete groups

Ernest Płonka (1997)

Annales Polonici Mathematici

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We present a new approach to determining supports of extreme, normed by 1, positive definite class functions of discrete groups, i.e. characters in the sense of E. Thoma [8]. Any character of a group produces a unitary representation and thus a von Neumann algebra of linear operators with finite normal trace. We use a theorem of H. Umegaki [9] on the uniqueness of conditional expectation in finite von Neumann algebras. Some applications and examples are given.

Mappings preserving zero products

M. A. Chebotar, W.-F. Ke, P.-H. Lee, N.-C. Wong (2003)

Studia Mathematica

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Let θ : ℳ → 𝓝 be a zero-product preserving linear map between algebras. We show that under some mild conditions θ is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, C*-algebras and W*-algebras.

A note on states of von Neumann algebras

Allah-Bakhsh Thaheem (1979)

Aplikace matematiky

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The author proves that on a von Neumann albebra (possibly of uncountable cardinality) there exists a family of states having mutually orthogonal supports (projections) converging to the identity operator.