Let S(H) be the unit sphere of a Hilbert space H and Up(H) thegroup of unitary operators in H such that u−1 belongs to the p-Schatten idealBp(H). This group acts smoothly and transitively in S(H) and endows it witha natural ...

Let H= H+⊕ H- be a fixed orthogonal decomposition of the complex separable Hilbert space H in two infinite-dimensional subspaces. We study the geometry of the set Pp of selfadjoint projections in the Banach algebra Ap= { ...

If X is the set of compact or p-Schatten operators over a complex Hilbert separable space H, we study the existence and characterization properties of Hermitian A∈X such that |||A|||≤|||A+D|||,for allD∈D(X) or equivalently ...

Let T∈ L(H), and let T=U|T|= |T*| U be the polar decomposition of T . Then, for every λ∈[0,1], the λ-Aluthge transform is defined by D λ (T )= |T| l U|T| 1-λ . We show that several properties which are known for the usual ...

Sea ([OMEGA], M, [my]) un espacio de medida dotado de una medida [sigma] --finita [my]. Si (x, y) [??] k(x, y) es una función medible de [OMEGA] x [OMEGA] en R (núcleo), demostraremos que el operador A definido por Af(x) ...

Let L2 be the Lebesgue space of square-integrable functions on the unit circle. We show that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of L2. We also ...

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in-Schatten ideals. In addition, we investigate the problem of characterization of norm-parallelism for bounded linear ...