Banach Space


Completeness
a complete normed space ( is a Banach space)

If satisfies , satisfying exists.

Linear operator
normed spaces
Operator : a mapping from to the elements of .
Linear operator :

scalars

Bounded:

Continuous:

Bounded linear operator space
: set of bounded linear operators from to
Addition:
  1. For ,
  2. : scalar
  3. : zero element of
    If , then is a zero element of .
From the definition of addition, is also a Banach space.

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