Complex analysis operator theory

  • What is the application of complex analysis in string theory?

    In modern times, it has become very popular through a new boost from complex dynamics and the pictures of fractals produced by iterating holomorphic functions.
    Another important application of complex analysis is in string theory which examines conformal invariants in quantum field theory..

  • In contemporary mathematics, operator theory is a branch of functional analysis that focuses on bounded and unbounded maps from a normed vector space (or a topological vector space) into another.
  • In modern times, it has become very popular through a new boost from complex dynamics and the pictures of fractals produced by iterating holomorphic functions.
    Another important application of complex analysis is in string theory which examines conformal invariants in quantum field theory.

Linear transformation between topological vector spaces

In functional analysis and operator theory, a bounded linear operator is a linear transformation mwe-math-element> between topological vector spaces (TVSs) mwe-math-element> and mwe-math-element> that maps bounded subsets of mwe-math-element> to bounded subsets of mwe-math-element>
If mwe-math-element> and mwe-math-element> are normed vector spaces, then mwe-math-element> is bounded if and only if there exists some mwe-math-element> such that for all mwe-math-element>

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