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Applications:

1. Banach Algebras

Banach Spaces are utilized in another concept of mathematics created by the same Stefan Banach: Banach Algebras. To understand this concept, we must first understand the basics of algebras over a field. An algebra over a field is a type of vector space that can be generated from two other vector spaces, also called a bilinear product. A Banach Algebra is defined to be associative, that is, containing usable operations of addition, multiplication, and scalar multiplication. A Banach Algebra is itself a Banach Space.

2. Weiner Algebra

Another application of Banach Spaces can be found in the Weiner Algebra. The fundamental concept within Weiner Algebras lies in Fourier Series. A Fourier series is a type of series that repeats at regular intervals using summated sinusoidal functions. They are said to be periodic. Some examples of Fourier series can be seen below.

File:FourierSeriesCBCP
Image by WolframMathWorld

The Weiner Algebra is simply the set of all absolutely converging Fourier series. It also is a Banach Space.

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Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.