School of Mathematics, Statistics and Physics

# Pure Maths (Analysis) - Michael Dritschel (Newcastle)

Products of positive operators

Date/Time: Monday 19 October, 3.00pm - Analysis Seminar

Venue: Zoom

Abstract: On finite dimensional spaces, it is not hard to see that an operator is the product of two positive operators if and only if it is similar to a positive operator.  Here, the class L+2\mathcal{L}^{+\,2} of  bounded operators on separable infinite dimensional Hilbert spaces which can be written as the product of two bounded positive operators is explored.  The structure is much richer, and connects (but is not equivalent to) quasi-similarity and quasi-affinity to a positive operator.  The (generalized) spectral properties of operators in L+2\mathcal{L}^{+\,2} are explained, along with membership in L+2\mathcal{L}^{+\,2} among special classes, including algebraic and compact operators.

This is joint work with Maximiliano Contino, Alejandra Maestripieri, and Stefania Marcantognini at CONICET, Buenos Aires, Argentina.