I have reading through various sources on linear functionals, but all seem somewhat inconsistent with regard to denoting the set of all linear functionals and the set(adsbygoogle = window.adsbygoogle || []).push({});

Also, what is the standard definition of a continuous linear functional? I really couldn't find much besides

this

Let ##f : V \rightarrow \mathbb{K}## be a linear functional. It is said to be continuous if and only if for every ##x \in V##, there exists a positive number ##M## such that

##\frac{|f(x)|}{||x||} \le M##

where ##||x||## is the norm of ##x##. The least such number ##M## is called the norm of ##F##, written as ##||f||##,

which comes from http://www.solitaryroad.com/c855.html

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# I A Question about Notation and Continuous Linear Functionals

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