A measure named for these functions is sandwiched between a linear operator and its adjoint to Naimark dilate a different measure into higher dimensions. In quantum information theory, one of these functions corresponding to a “typical” space satisfies a lower bound trace condition of “one minus epsilon” asymptotically. Positive operator-valued measures, or P·O·V·Ms, (*) generalize a type of measure that maps from sets to these functions. The density matrix for a pure state, but not a mixed state, is one of these functions. (-5[1])One of these functions can be written as “ket psi bra psi.” (10[1])A namesake “postulate” of (-5[1])quantum (10[1])mechanics treats measurement as applying (-5[1])one of these operators for a given eigenstate. For 10 points, name these idempotent operators that map onto a subspace. (10[1])■END■ (10[4]0[2])