Displaying similar documents to “Jucys-Murphy elements and the unitary Weingarten function”

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. ...

Geometric characterization of L₁-spaces

Normuxammad Yadgorov, Mukhtar Ibragimov, Karimbergen Kudaybergenov (2013)

Studia Mathematica

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The paper is devoted to a description of all real strongly facially symmetric spaces which are isometrically isomorphic to L₁-spaces. We prove that if Z is a real neutral strongly facially symmetric space such that every maximal geometric tripotent from the dual space of Z is unitary, then the space Z is isometrically isomorphic to the space L₁(Ω,Σ,μ), where (Ω,Σ,μ) is an appropriate measure space having the direct sum property.

On isometries of the symmetric space P₁(3,ℝ)

Gašper Zadnik (2014)

Colloquium Mathematicae

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We classify the isometries in the non-identity component of the whole isometry group of the symmetric space of positive 3 × 3 matrices of determinant 1: we determine the translation lengths, minimal spaces and fixed points at infinity.

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'.

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.