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On the Moore-Penrose inverse in C*-algebras.

Enrico Boasso (2006)

Extracta Mathematicae

In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra...

On the powers of Voiculescu's circular element

Ferenc Oravecz (2001)

Studia Mathematica

The main result of the paper is that for a circular element c in a C*-probability space, ( c ⁿ , c n * ) is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.

On the quantum groups and semigroups of maps between noncommutative spaces

Maysam Maysami Sadr (2017)

Czechoslovak Mathematical Journal

We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are...

On the structural theory of  II 1 factors of negatively curved groups

Ionut Chifan, Thomas Sinclair (2013)

Annales scientifiques de l'École Normale Supérieure

Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor L Γ is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that L Γ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in  Sp ( n , 1 ) , n ≥ 2 , are virtually W * -superrigid.

On the transient and recurrent parts of a quantum Markov semigroup

Veronica Umanità (2006)

Banach Center Publications

We define the transient and recurrent parts of a quantum Markov semigroup 𝓣 on a von Neumann algebra 𝓐 and we show that, when 𝓐 is σ-finite, we can write 𝓣 as the sum of such semigroups. Moreover, if 𝓣 is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state ρₙ, we find conditions under which any normal invariant state is a convex combination of ρₙ's.

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