Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

47Kxx Operator theory in abstract spaces

This subtopic introduces the core ideas in operator theory in abstract spaces, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

47K05 General theory of graphs of linear operators

Overview

The general theory of graphs of linear operators studies the relationship between an operator and its graph, providing a geometric viewpoint on closed operators.

Related Wikipedia Page

Closed graph theorem

Useful Links

Key Ideas

  • Closed operators
  • Graph norms
  • Operator domain structure

Typical Uses

Used in functional analysis to characterize operators whose domains and ranges are compatible with topological structure.

Applications

  • Unbounded operators
  • Differential operators
  • Spectral theory

References

Recommended Textbooks