Let U2 (H) be the Banach-Lie group of unitary operators in the Hilbert space H which are Hilbert-Schmidt perturbations of the identity 1. In this paper we study the geometry of the unitary orbit{u p u* : u ∈ U2 (H)}, of ...

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 ...

Let A be a positive injective operator in a Hilbert space View the MathML source, and denote by View the MathML source the inner product defined by A : [f,g]=〈Af,g〉. A closed subspace S⊂H is called A -compatible if ...

We study the set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin ...

Let H = H+ ⊕ H− be a fixed orthogonal decomposition of a Hilbert space, with both subspaces of infinite dimension, and let E+, E− be the projections onto H+ and H−. We study the set Pcc of orthogonal projections P in H ...

We obtain a characterization of theta functions of Jacobian varieties of curves with automorphisms among theta functions of principally polarized abelian varieties (p p a v) We first give a characterization m terms of ...