Spectral systems with the one-way spectral mapping property
Keywords: Banach algebra, spectral system, joint spectrum
For Banach algebras we characterize spectral systems which satisfy the one-way spectral mapping property. We show that these spectral systems are determined by projective systems of multiplicative linear functionals of finitely generated subalgebras and, using this, we derive several consequences concerning multiplicative extensions of multiplicative linear functionals of subalgebras.
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