Operator Theory

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5 domain-specific abstractions whose origin domain is Operator Theory.

• Holomorphic functional calculus — A calculus assigning f(T) to a bounded operator T for every function holomorphic near its spectrum through a contour integral of the resolvent.
• Hyponormal operator — A bounded Hilbert-space operator whose self-commutator TT−TT is positive semidefinite.
• Pseudospectrum — For an operator and tolerance epsilon, the set of spectral values attainable under perturbations of size epsilon, equivalently points where the resolvent is large.
• Spectral abscissa — The greatest real part among the eigenvalues or spectral values of a matrix or bounded linear operator.
• Toeplitz operator — The compression to Hardy space of multiplication by a bounded function on the unit circle, yielding an operator with constant matrix diagonals.