Does this equality hold: $(UAU^{-1})^* = UA^*U^{-1}$? where $U$ is invertible. Suppose these operators are defined on a Banach space.
2026-03-26 06:34:21.1774506861
Adjoints of similar operators
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In general $(UAU^{-1})^* = UA^*U^{-1}$ is not correct.
Correct is: $(UAU^{-1})^* =(U^*)^{-1}A^*U^*$