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Andriamanankasina Ramanantoanina (CEU): Functional Representations of Positive Operators

 Kedd, 3. December 2019, 10:00 - 11:00
Given a Hilbert space $H$, a selfadjoint operator $A$ on $H$ is uniquely defined by its projection valued measure $E_A$, its so-called spectral measure. Partial orders on selfadjoint operators can be defined:

1) the usual order: $A \leq B$ when $\langle Ax, x\rangle \leq \langle Bx, x\rangle$ for all $x\in H$.

2) the spectral order: $A \preceq B$ when $E_B((-\infty,t]) \leq E_A((-\infty,t])$ for all $t\in\mathbb{R}$.

The set of positive operators on $H$ can be embedded into the set of real valued functions on the unit sphere of $H$ in a way that preserves these orders. We will study some concrete examples of these embedding and their properties. We will present an application in the computation of spectral order automorphism of subsets of the selfadjoint operators.
Hely : Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged