With these definitions, the "resolvent set" of "T" is the set of all complex numbers ζ such that "Rζ" exists and is bounded. This set often is denoted as "ρ(T)". The "spectrum" of "T" is the set of all complex numbers ζ such that "Rζ" fails to exist or is unbounded. Often the spectrum of "T" is denoted by "σ(T)". The function "Rζ" for all ζ in "ρ(T)" (that is, wherever "Rζ" exists as a bounded operator) is called the resolvent of "T". The "spectrum" of "T" is therefore the complement of the "resolvent set" of "T" in the complex plane. Every eigenvalue of "T" belongs to "σ(T)", but "σ(T)" may contain non-eigenvalues.