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...algebra|derivation]]s from ''A'' into [[dual module|dual]] [[Banach module|Banach ''A''-bimodules]] are [[inner derivation|inner]] (that is of the form <math ...continuous algebra homomorphism <math>\theta</math> from ''A'' to another Banach algebra, then the closure of <math>\overline{\theta(A)}</math> is amenable. ...

In [[mathematics]], '''Banach algebra cohomology''' of a [[Banach algebra]] with coefficients in a bimodule is a [[cohomology]] theory define ...itation | last1=Johnson | first1=Barry Edward | title=Cohomology in Banach algebras | url=https://books.google.com/books?id=WgYuKl1Y340C | publisher=[[American ...

...'', together with a [[norm (mathematics)|norm]] on ''A'' that makes it a [[Banach algebra]]. ...mple Banach algebra is [[isomorphic]] (via the [[Gelfand transform]]) to a Banach function algebra on its [[character space]] (the space of algebra homomorph ...

{{About|the Banach algebra concept||Approximation to the identity (disambiguation){{!}}Approxi ...ng theory]], an approximate identity is a [[net (mathematics)|net]] in a [[Banach algebra]] or [[ring (mathematics)|ring]] (generally without an identity) th ...

...]] [[isomorphic]] to the [[complex number]]s, i.&nbsp;e., the only complex Banach algebra that is a [[division algebra]] is the complex numbers '''C'''. ...a complex Banach algebra is nonempty: for every element ''a'' of a complex Banach algebra ''A'' there is some complex number ''λ'' such that ''λ''1&nbsp;&m ...

...gical]] [[Hausdorff space]], such that each fiber has the structure of a [[Banach space]]. ...jection]], such that each '''fiber''' <math>B_x := \pi^{-1}(x)</math> is a Banach space. Which satisfies the following conditions: ...

...], is a vector space equipped with a bilinear vector product. Some notable algebras in this sense are: ...ative ring]], a module equipped with a bilinear product. Generalization of algebras over a field ...

...are determined to a large extent by their projections. The idea behind AW*-algebras is to forgo the former, topological, condition, and use only the latter, al Hence an AW*-algebra is a C*-algebras that is at the same time a [[Baer *-ring]]. ...

...n theorem''' states that if <math> V </math> is a [[left module]] over a [[Banach algebra]] <math> B </math> with a left approximate unit <math> (u_{i})_{i \ |title = Factorization in group algebras ...

...tudy, Princeton | zbl=0095.10103 | year=1957 | volume=2 | chapter=Function algebras | pages=213–226}} *''Completely Bounded Maps and Operator Algebras'' Vern Paulsen, 2002 {{ISBN|0-521-81669-6}} ...

In [[operator theory]], a branch of mathematics, every [[Banach algebra]] can be associated with a group called its '''abstract index group Let ''A'' be a Banach algebra and ''G'' the group of invertible elements in ''A''. The set ''G'' ...

In mathematics, the term '''Beurling algebra''' is used for different algebras introduced by {{harvs|txt=yes|first=Arne|last=Beurling|authorlink=Arne Beu is a [[Unitary group|unitary]] [[commutative]] [[Banach algebra]]. ...

Rickart did research on [[Banach algebra]]s and was the author of three books. In the late 1950s and early 1 ...cite journal|author=Yood, Bertram|title=Review: ''General theory of Banach algebras'' by C. E. Rcikart|journal=Bull. Amer. Math. Soc.|year=1961|volume=67|issue ...

...e it is given by a [[universal property]]; and (as always with von Neumann algebras) the term ''W*-algebra'' may be used in place of ''von Neumann algebra''. ...*-algebra ''A'', ''A''**, can be identified with ''A''&prime;&prime;, as [[Banach space]]s. ...

...]]s on [[topological space]]s, named after the [[mathematician]]s [[Stefan Banach]] and [[Marshall Stone]]. ...d with the weak*-topology inherited from the dual space ''C''(''X'')*. The Banach-Stone theorem avoids reference to multiplicative structure by recovering '' ...

where {{math|''H''^&infin;('''D''')}} denotes the Banach space of bounded analytic functions on the unit disc '''D''' (i.e. a [[Hard by construction it becomes a [[uniform algebra]] and a commutative [[Banach algebra]]. ...

...ere he earned his [[PhD]] with the dissertation '' Generalized Convolution Algebras and Spectral Representations'' supervised by [[Cassius Ionescu-Tulcea]]. Du [[Banach algebra|Banach]]-algebras, integral representations in convex sets, and Korovkin theory. ...

...finite]].<ref>{{citation|title=Banach Algebras and the General Theory of *-Algebras, Volume 2|series=Encyclopedia of mathematics and its applications|volume=79 | contribution = Deformation and rigidity for group actions and von Neumann algebras ...

...ete [[Norm (mathematics)|normed field]]) that at the same time is also a [[Banach space]], that is, a [[normed space]] that is [[complete metric space|comple A Banach algebra is called ''unital'' if it has an [[identity element]] for the mult ...

...the [[holomorphic functional calculus]]. Hypercomplex analysis on Banach algebras is called [[functional analysis]]. ...