Introduction

This post gives an entry to the Banach Spaces in Functional Analysis.

Abstract

A space is considered a Banach Space if its normed spaces and their properties are complete in the metric induced by its norm. The two first indices of the norm are called equivalent if and only if they give the same topology, which is equivalent to the existence of constants 'c', for C > 0.

References

• [1] https://mathworld.wolfram.com/BanachSpace.html
• [2] https://www.math.stonybrook.edu/~joa/PUBLICATIONS/SOBOLEV.pdf