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Let W(A) and $W_e\left(A\right)$ be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A₁, ..., Aₘ) acting on an infinite-dimensional Hilbert space. It is shown that $W_e\left(A\right)$ is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ 1, ..., m, $W_e\left(A\right)$ can be obtained as the intersection of all sets of the form $cl\left(W(A₁,...,A_{i+1},A_i+F,A_{i+1},...,Aₘ)\right)$, where F = F* has finite rank. Moreover, the closure cl(W(A)) of W(A) is always star-shaped with the elements in $W_e\left(A\right)$ as star centers....