by Henri Lebesgue. This was later formalized by Banach and Hilbert, around 1920. At that time, algebra and the new field of functional analysis began to...

ISBN 978-0-8247-8419-5 Lang, Serge (1987), Linear algebra, Berlin, New York: Springer-Verlag, ISBN 978-0-387-96412-6 Banach, Stefan (1922), "Sur les opérations dans...

{\displaystyle \mathbb {RFM} _{I}(R)} of row finite matrices. If R is a Banach algebra, then the condition of row or column finiteness in the previous point...

octonions). The quaternions are also an example of a composition algebra and of a unital Banach algebra. Because the product of any two basis vectors is plus or...

rings that appear in analysis are noncommutative. For example, most Banach algebras are noncommutative. The set of natural numbers ⁠ N {\displaystyle \mathbb...

Mathematical Physics Algebra & Number Theory Algebra Colloquium Algebra i Logika Algebra Universalis Algebraic & Geometric Topology Algebraic Combinatorics American...

branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus...

an algebra. This property follows directly from the fact that BV ⁡ ( Ω ) {\displaystyle \operatorname {\operatorname {BV} } (\Omega )} is a Banach space...

Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives. It is named after Francesco Faà di Bruno (1855...

\|f\|_{1}\|g\|_{p}.} In the particular case p = 1, this shows that L1 is a Banach algebra under the convolution (and equality of the two sides holds if f and...