Displaying similar documents to “Unitary dilation and fixed point theorem”

Unitary equivalence of operators and dilations

Chafiq Benhida (2004)

Studia Mathematica

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Given two contractions T and T' such that T'-T is an operator of finite rank, we prove, under some conditions, the unitary equivalence of the unitary parts of the minimal isometric dilations (respectively minimal co-isometric extensions) of T and T'.

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. ...

On operators with unitary ϱ-dilations

T. Ando, K. Takahashi (1997)

Annales Polonici Mathematici

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We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class C ϱ , then T itself is unitary.