Working in Operator Theory (Preliminary)

Getting started

• Take as much linear algebra as possibe

  • Horn and Garcia’s A Second Course in Linear Algebra

  • Sergei Treil’s Linear Algebra Done Wrong

• Take as much complex analysis as possible

  • Donald Sarason’s Complex Function Theory is a short and self-contained one semester introduction

  • A First Course in Complex Analysis by Beck, Marchesi, Pixton, and Sabalka

• Read Sheldon Axler’s Linear Algebra Done Right if you didn’t use it for your second linear algebra course

  • http://linear.axler.net A complete video lecture series by Sheldon Axler and other resources

• Follow up with Nicholas Young’s Introduction to Hilbert Space

  • Hilbert Space: a sequel to linear algebra online text adapted from and inspired by Introduction to Hilbert Space by Ryan Tully-Doyle

Graduate school

• Ideally, you’ll take a year each of real, complex, and functional analysis

• Consider matrix theory, harmonic analysis, PDE, probability, and abstract algebra

• Learn some mathematical programming - many hypotheses in functional operator theory can be tested on examples