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Sphere and projective space of a C*-algebra with a faithful state

100%

Antunez A. C.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

410--427

Let A be a unital C*-algebra with a faithful state φ. We study the geometry of the unit sphere Sφ = {x∈A : φ(x*x) = 1} and the projective space Pφ = Sφ/T. These spaces are shown to be smooth manifolds and homogeneous spaces of the group Uφ(A) of isomorphisms acting in A which preserve the inner product induced by φ, which is a smooth Banach-Lie group. An important role is played by the theory of operators in Banach spaces with two norms, as developed by M.G. Krein and P. Lax. We define a metric in Pφ, and prove the existence of minimal geodesics, both with given initial data, and given endpoints.

A characterization of completely bounded multipliers of Fourier algebras

94%

Jolissaint P.

nr 2

311-313

Range projections of idempotents in C*-algebras

94%

Koliha J.

2001

tom Vol. 34, nr 1

91-103

In this paper we study range projections of idempotents m C*-algebras, and use them to obtain a Schur type decomposition that leads to simple proofs of results on Moore-Penrose inverse and norms of idempotents. We analyze the continuity of range projections, obtain a general result on their approximation, and recover a result of Vidav on two projections in a Hilbert space. Several representations of range projections are given.

Elements of C*-algebras commuting with their Moore-Penrose inverse

94%

Koliha J. J.

Studia Mathematica

2000

tom 139

nr 1

81-90

We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.

A note on Radon-Nikodym derivatives and similarity for completely bounded maps

94%

Gheondea A. , Kavruk A. S.

Opuscula Mathematica

2009

tom Vol. 29, no. 2

139-145

We point out a relation between the Arveson's Radon-Nikodym derivative and known similarity results for completely bounded maps. We also consider Jordan type decompositions coming out from Wittstock's Decomposition Theorem and illustrate, by an example, the nonuniqueness of these decompositions.

Operators preserving ideals in C*-algebras

94%

S. Shul'Man V.

nr 1

67-72

The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.