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ON THE HAHN-BANACH THEOREM
2007
Advanced Courses of Mathematical Analysis II
I love the Hahn-Banach theorem. I love it the way I love Casablanca and the Fontana di Trevi. It is something not so much to be read as fondled. What is "the Hahn-Banach theorem?" Let f be a continuous linear functional defined on a subspace M of a normed space X. Take as the Hahn-Banach theorem the property that f can be extended to a continuous linear functional on X without changing its norm. Innocent enough, but the ramifications of the theorem pervade functional analysis and other
doi:10.1142/9789812708441_0006
fatcat:ist2ruscmze4xlj4mii3tofc3e