On the joint spectra of operators and antiunitaries

Key Points

• The antiunitary operator transforms the Taylor spectrum of commuting operators, changing its properties significantly.
• The main finding shows that the spectrum of the transformed operator matches the conjugate of the original operator's spectrum.
• Analysis reveals the identical relationship for the Xia spectrum under the action of the antiunitary operator.
• These findings may suggest deeper connections in spectral theory and potentially influence future studies in quantum mechanics.