Thomas Streicher: An Effective Spectral Theorem for Bounded Self Adjoint Operators

Datum objave: 20. 6. 2016
Seminar za temelje matematike in teoretično računalništvo
Torek, 21. 6. 2016, od 12h do 14h, Plemljev seminar, Jadranska 19

Speaker: Prof. Thomas Streicher, Technical University of Darmstadt, Germany.

(Joint work with M. Pape.)

Title: An Effective Spectral Theorem for Bounded Self Adjoint Operators

We show that bounded self adjoint operators on Hilbert space correspond in a computable way to so-called "spectral valuations" on compact intervals of reals. The underlying model of computable analysis are admissible representations and maps between them having effective realizers.

As a byproduct we identify the topologies induced by the admissible representaions. Luckily they are not too different from what's considered traditionally in the literature.