What does banach algebra mean?
Definitions for banach algebra
ba·nach al·ge·bra
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Wikidata
Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers that at the same time is also a Banach space, i.e. normed and complete. The algebra multiplication and the Banach space norm are required to be related by the following inequality: . This ensures that the multiplication operation is continuous. This property is found in the real and complex numbers; for instance, |-6×5| ≤ |-6|×|5|. If in the above we relax Banach space to normed space the analogous structure is called a normed algebra. A Banach algebra is called "unital" if it has an identity element for the multiplication whose norm is 1, and "commutative" if its multiplication is commutative. Any Banach algebra can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of . Often one assumes a priori that the algebra under consideration is unital: for one can develop much of the theory by considering and then applying the outcome in the original algebra. However, this is not the case all the time. For example, one cannot define all the trigonometric functions in a Banach algebra without identity.
Numerology
Chaldean Numerology
The numerical value of banach algebra in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of banach algebra in Pythagorean Numerology is: 3
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"banach algebra." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/banach+algebra>.
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