# Banach algebra

(redirected from B-algebra)

## Banach algebra

[′bä‚näk ′al·jə·brə]
(mathematics)
An algebra which is a Banach space satisfying the property that for every pair of vectors, the norm of the product of those vectors does not exceed the product of their norms.

## Banach algebra

(mathematics)
An algebra in which the vector space is a Banach space.
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(see ) extended the concept of cubic set to subalgebras, ideals and closed ideals of B-algebra with lots of properties investigated.
A B-algebra is an important class of logical algebras introduced by Neggers and Kim  and extendedly investigated by several researchers.
A non-empty set X with constant 0 and a binary operation x is called to be B-algebra  if it satisfies the following axioms:
A non-empty subset S of B-algebra X is called a subalgebra  of X if x x y [member of] S [for all] x, y [member of] S.
 defined the cubic subalgebras of B-algebra by combining the definitions of subalgebra over crisp set and the cubic sets.
Let X denote a B-algebra then the concept of cubic subalgebra can be extended to neutrosophic cubic subalgebra.
Example 3.1 Let X = (0, [a.sub.1], [a.sub.2], [a.sub.3], [a.sub.4], [a.sub.5]} be a B-algebra with the following Cayley table.
Example, let X = (0, [a.sub.1], [a.sub.2], [a.sub.3], [a.sub.4], [a.sub.5]} be a B-algebra with the following Caley table.
Proof: Let X be a B-algebra and x, y [member of] X.
Example 3.2 Let X = (0, [a.sub.1], [a.sub.2], [a.sub.3], [a.sub.4], [a.sub.5]} be a B-algebra in Remark 3.1 and A = ([A.sub.T,I,F], [[lambda].sub.T,I,F]) is a neutrosophic cubic set defined by
Definition 4.1 A neutrosophic cubic set A=([A.sub.T,I,F], [[lambda].sub.T,I,F]) in the B-algebra X is said to have rsup-property and inf-property if for any subset S of X, there exist [s.sub.0] [member of] T such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Theorem 4.4 suppose f | X [right arrow] Y be a homomorphism from a B-algebra X onto a B-algebra Y.

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