Banach Envelopes of Non-Locally Convex Spaces

Source abstract

Let X be a quasi-Banach space whose dual X * separates the points of X . Then X * is a Banach space under the norm From X we can construct the Banach envelope X c of X by defining for x ∊ X , the norm Then X c is the completion of ( X , ‖ ‖ c ). Alternatively ‖ ‖ c is the Minkowski functional of the convex hull of the unit ball. X c has the property that any bounded linear operator L:X → Z into a Banach space extends with preservation of norm to an operator .