Partial isometries and pseudoinverses in semi-Hilbertian spaces

MARÍA CELESTE GONZALEZ

Münster

Conferencia; Young mathematicians in C*-algebras; 2016

Universidad de Munster

Let H be a Hilbert space with inner product 〈,〉 and B(H) the algebra ofbounded linear operators on H . Given a positive operator A ∈ B(H), ­_A=defines a semi-inner product on H and (H ,〈,〉_A) is called a semiHilbertianspace. An operator T∈ B(H) is an A-partial isometry if ||T x||_A =||x||_A for all ξ ∈ Ker(AT)^{ot_A}. This definition does not allow to ensure that an A-partial isometry admits an adjoint operator respecto to 〈,〉_A. Therefore, it is not trivial how to extend the well known equivalences for partial isometriesto A-partial isometries. In this talk we will study different equivalentconditions for an operator to be an A-partial isometry