Dual space definition in real analysis with example
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Dual space (functional analysis)

In mathematics, particularly in the branch offunctional analysis, a dual space refers to the space of all continuous linear functionals on a real or complex Banach space. The dual space of a Banach space is again a Banach space when it is endowed with the operator norm. If Xis a Banach space then its dual space is often denoted by X'.
Contents
1 Definition2 The bidual space and reflexive Banach spaces3 Dual pairings4 References5 Further reading
[edit]Definition
Let X be a Banach space over a field F which is real or complex, then the dual space X' of  is the vector space over F of all continuous linear functionals  when F is endowed with the standard Euclidean topology.
The dual space  is again a Banach space when it is endowed with the operator norm. Here the operator norm  of an element  is defined as:

where  denotes the norm on X.
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In mathematics, particularly in the branch offunctional analysis, a dual space refers to the space of all continuous linear functionals on a real or complex Banach space. The dual space of a Banach space is again a Banach space when it is endowed with the operator norm. If Xis a Banach space then its dual space is often denoted by X'.
Contents
1 Definition2 The bidual space and reflexive Banach spaces3 Dual pairings4 References5 Further reading
[edit]Definition
Let X be a Banach space over a field F which is real or complex, then the dual space X' of  is the vector space over F of all continuous linear functionals  when F is endowed with the standard Euclidean topology.
The dual space  is again a Banach space when it is endowed with the operator norm. Here the operator norm  of an element  is defined as:

where  denotes the norm on X.
please mark as brainliest please please
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