A note on the linear cycle space for groups of Hermitian type.

Wolf, Joseph A.; Zierau, Roger

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In this paper, we construct a hyperkähler structure on the complexification $𝒪^{ℂ}$ of any Hermitian symmetric affine coadjoint orbit $𝒪$ of a semi-simple $L^{*}$ -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of $𝒪$ . By a relevant identification of the complex orbit $𝒪^{ℂ}$ with the cotangent space $T 𝒪$ of $𝒪$ induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on $T 𝒪$ compatible...

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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...