A-Spectral Permanence Property for $$C^*$$ -Algebras
Tóm tắt
For a positive element A of a
$$C^*$$
-algebra
$$\mathfrak {A}$$
, let
$${\Vert X\Vert }_{A}$$
denote the A-operator semi-norm of
$$X\in \mathfrak {A}$$
. In this paper, we aim to introduce and study the notion of A-spectrum for X, such that
$${\Vert X\Vert }_{A}<\infty $$
. In particular, when A is well supported, we establish an A-spectral permanence property for
$$C^*$$
-algebras.
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