Displaying similar documents to “Groups of isometries on operator algebras”

Isometries of the unitary groups in C*-algebras

Osamu Hatori (2014)

Studia Mathematica

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We give a complete description of the structure of surjective isometries between the unitary groups of unital C*-algebras. While any surjective isometry between the unitary groups of von Neumann algebras can be extended to a real-linear Jordan *-isomorphism between the relevant von Neumann algebras, this is not the case for general unital C*-algebras. We show that the unitary groups of two C*-algebras are isomorphic as metric groups if and only if the C*-algebras are isomorphic in the...

Wold-type extension for N-tuples of commuting contractions

Marek Kosiek, Alfredo Octavio (1999)

Studia Mathematica

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Let (T1,…,TN) be an N-tuple of commuting contractions on a separable, complex, infinite-dimensional Hilbert space ℋ. We obtain the existence of a commuting N-tuple (V1,…,VN) of contractions on a superspace K of ℋ such that each V j extends T j , j=1,…,N, and the N-tuple (V1,…,VN) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the V j need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])

Characterization of unitary processes with independent and stationary increments

Lingaraj Sahu, Kalyan B. Sinha (2010)

Annales de l'I.H.P. Probabilités et statistiques

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This is a continuation of the earlier work ( (2009) 745–785) to characterize unitary stationary independent increment gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson–Parthasarathy equation is proved.

A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

Charles Batty, Zdzisław Brzeźniak, David Greenfield (1996)

Studia Mathematica

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Let T be a semigroup of linear contractions on a Banach space X, and let X s ( T ) = x ∈ X : l i m s → ∞ ∥ T ( s ) x ∥ = 0 . Then X s ( T ) is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then X s ( T ) is the annihilator of the unitary eigenvectors of T*, and l i m s ∥ T ( s ) x ∥ = i n f ∥ x - y ∥ : y ∈ X s ( T ) for each x in X.

Unitary Banach algebras

Julio Becerra Guerrero, Simon Cowell, Ángel Rodríguez Palacios, Geoffrey V. Wood (2004)

Studia Mathematica

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In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the C*-algebras and the ℓ₁ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of C*-algebras are given. ...