TL;DR
This paper investigates the maximum number of orthogonal conjugations in Hilbert spaces, establishing bounds and showing they are achieved when the space's dimension is a power of two, leaving other dimensions as open problems.
Contribution
It provides bounds for the number of orthogonal conjugations and proves their saturation in spaces with dimensions that are powers of two.
Findings
Bounds for the number of orthogonal conjugations are established.
Saturation of bounds occurs when the Hilbert space dimension is a power of two.
Open problem remains for other dimensions.
Abstract
After a short introduction to anti-linearity, bounds for the number of orthogonal (skew) conjugations are proved. They are saturated if the dimension of the Hilbert space is a power of two. For the other dimensions this is an open problem.
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