This talk will be an elementary introduction to (Hilbert) module approach to operator theory. We explore the relationship of the classical von Neumann-Wold decomposition theorem and the Beurling-Lax-Halmos theorem for isometries. We will also discuss a unified approach to the invariant subspace problem for bounded linear operators on Hilbert spaces. The talk will be accessible to a general audience including graduate students.

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Last updated: 22 Feb 2019