The commutation principle of Ramírez et al. (SIAM J Optim 23:687–694, 2013) proved in the setting Euclidean Jordan algebras says that when sum a real valued function h and spectral $$\Phi $$ is minimized/maximized over set E, any local optimizer at which Fréchet differentiable operator commutes with derivative $$h^{\prime }(a)$$ . In this note, we describe some analogs above result by assuming ...

This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product L⊗̂J , and that the obstruction for the comparison map K(L⊗̂J ) → K(...

Abstract Inspired by this felicitous, highly concentrated and rather exhaustive review of a rapidly growing field, many larger research areas that warrant further investigation come to mind. In comment, three are selected: fully satisfactory PCA on tori polyspheres, harnessing linearity through Lie algebras underlying homogeneous spaces such as those for directional data, statistical analysis b...

The work is devoted to the study of Fréchet algebras symmetric (invariant under composition every components its argument with any measure preserving bijection domain argument) analytic functions on Cartesian powers complex Banach spaces Lebesgue integrable in a power $p\in [1,+\infty)$ complex-valued segment $[0,1]$ and semi-axis. We show that algebra all entire bounded type $n$th space $L_p[0...