Gowda, MuddappaJeong, Juyoung2018-08-012018-08-012018http://hdl.handle.net/11603/11036Let V be a Euclidean Jordan algebra of rank n. A set E in V is said to be a spectral set if there exists a permutation invariant set Q in Rn such that E = λ−1(Q), where λ : V → Rn is the eigenvalue map that takes x ∈ V to λ(x) (the vector of eigenvalues of x written in the decreasing order). If the above Q is also a convex cone, we say that E is a spectral cone. This paper deals with connectedness and arcwise connectedness properties of spectral sets. By relying on the result that in a simple Euclidean Jordan algebra, every eigenvalue orbit [x] := {y : λ(y) = λ(x)} is arcwise connected, we show that if a permutation invariant set Q is connected (arcwise connected), then λ−1(Q) is connected (respectively, arcwise connected). A related result is that in a simple Euclidean Jordan algebra, every pointed spectral cone is irreducible.14 pagesen-USThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please contact the author.Euclidean Jordan algebraspectral setconnectednessirreducible coneText