The norm is a real valued function, the range of the bounded linear functionals is the field of complex numbers. In your demonstration of boundedness, you are comparing the size of a real number to a complex number, which doesn't make sense. You need the magnitude of the complex number in front of the norm.
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Brian G. Valentine +2
The norm is a real valued function, the range of the bounded linear functionals is the field of complex numbers. In your demonstration of boundedness, you are comparing the size of a real number to a complex number, which doesn't make sense. You need the magnitude of the complex number in front of the norm.
2 месяца назад